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RRED Indices: Reduced Reference Entropic Differencing for Image Quality Assessment
Abstract
We study the problem of automatic "reduced-reference" image quality assessment (QA) algorithms from the point of view of image information change. Such changes are measured between the reference- and natural-image approximations of the distorted image. Algorithms that measure differences between the entropies of wavelet coefficients of reference and distorted images, as perceived by humans, are designed. The algorithms differ in the data on which the entropy difference is calculated and on the amount of information from the reference that is required for quality computation, ranging from almost full information to almost no information from the reference. A special case of these is algorithms that require just a single number from the reference for QA. The algorithms are shown to correlate very well with subjective quality scores, as demonstrated on the Laboratory for Image and Video Engineering Image Quality Assessment Database and the Tampere Image Database. Performance degradation, as the amount of information is reduced, is also studied.
Overview
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TL;DR
The paper introduces RRED indices, reduced-reference image quality assessment algorithms that measure average absolute differences between scaled wavelet-domain entropies of a reference image and a Gaussian-scale-mixture natural-image approximation of the distorted image. Across LIVE and TID2008, the indices correlate well with subjective scores and degrade gracefully as reference information is reduced, with some variants approaching full-reference performance.
Key findings
- On LIVE, RRED M16/16 achieved overall SROCC 0.9429 and LCC 0.9385 using L/36 scalars, compared with PSNR SROCC 0.8754 and VIF (FR) SROCC 0.9636; RRED M10/10 achieved overall SROCC 0.9343 using L/144 scalars.
- Filtering and subsampling reduced reference information but degraded overall SROCC from 0.9429 at L/36 to 0.8543 at L/9296.
- Single-number algorithms had overall SROCC 0.7682 for σ²W = 0, 0.7978 for σ²W = 0.1, and 0.8877 for σ²W = 1; RRED* using 4 numbers achieved overall SROCC 0.8606, outperforming WNISM (0.7651) but below Curvelet (0.9104) and HWD2 (0.9418).
- On TID2008, RRED M16/16 achieved overall SROCC 0.824, above VIF (0.750), VSNR (0.705), PSNR (0.553), and WNISM (0.512), but below MSSIM (0.853); RRED 1/22 achieved 0.521.
Methods
- The RRED family computes the average absolute difference between scaled entropies of wavelet coefficients after an additive Gaussian neural noise channel, modeling both reference and distorted wavelet coefficients as Gaussian scale mixtures; algorithms vary by subband and by the amount of reference information via filtering/subsampling.
- Experiments used LIVE (779 distorted images, five distortion categories) and TID2008 (17 distortion types, 1700 distorted images), with a steerable pyramid decomposition using 6 orientations at 4 scales (25 subbands), 3×3 blocks (N = 9), and σ²W = 0.1 except in the single-number noise study; parameters were estimated by maximum likelihood without database training.
- Performance was assessed with Spearman rank-order correlation (SROCC) and linear correlation coefficient (LCC) after logistic nonlinearity against subjective DMOS/MOS, compared with PSNR, VIF, MSSIM, VSNR, WNISM, Curvelet, and HWD2.
Limitations
- The paper states that overall performance of single-number algorithms may be improved by better aligning scores across distortion categories, that multiscale decomposition increases complexity and needs efficient implementations, and that dependence on viewing distance requires better understanding; future work includes video.
- The paper reports that performance degrades with subsampling and that single-number algorithms are sensitive to neural noise variance; Gaussian blur performance decreases as σ²W increases (0.9698 at 0, 0.9038 at 0.1, 0.6108 at 1).
- Evident from reported tables, though not framed as limitations by the authors: RRED* overall SROCC 0.8606 is lower than Curvelet 0.9104 and HWD2 0.9418 on LIVE, and TID2008 RRED M16/16 is below MSSIM overall (0.824 vs 0.853) with low SROCC for mean shift (0.538) and contrast change (0.542).
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28 Own interpretation · 20 No basis given · 17 Own result · 11 Not checked yet · 3 Own method · 2 Sources not found
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“This procedure results in loss of performance with subsampling as illustrated in Section V.”
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- The authors state this as an assumption: Non-overlapping blocks of wavelet coefficients are independent and identically distributed.
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“It turns out that these algorithms are more sensitive to the choice of the neural noise variance.”
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“Further, we observe that the performance obtained by choosing the vertical subbands is marginally better than the horizontal subbands.”
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“As we move from (a) to (d), the RRED indices are now evaluated in finer scales, which provide a better separation of quality scores.”
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“Even when only a single scalar is obtained from the reference image, the algorithm achieves close to state of the art performance within each distortion category without knowing anything about the type of distortions that the image might have been subjected to.”
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“Moreover, the algorithms perform much better than mean squared error, which is an FR algorithm.”
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“Certain distortions such as JPEG and JPEG2000 lead to different locations in the same subband having an increase and decrease in entropy simultaneously.”
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“The only drawback of the algorithm is the reduced performance in the category of images corrupted by fast fading errors.”
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“One important observation is that some of the RRED indices perform nearly as well as the best performing FR QA algorithms such as VIF.”
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“Table III clearly demonstrates the degradation in the performance of the RR algorithms with subsampling.”
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“Thus the overall computational complexity of the RRED algorithms is O ( N (log N + M 2 )) .”
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“The correlation analysis reveals that subbands at certain scales are more sensitive to particular distortions or artifacts.”
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“For example, by using 4 numbers from the four vertical subbands at different scales of the reference, we can improve the overall SROCC for σ 2 W = 0 . 1 to 0.8606 by weighting the bands from coarser scales to the finer scales in the ratio 8:4:2:1.”
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“One of the bottle necks in the computation of the RRED indices is the time required to perform a multiscale multiorientation decomposition using steerable pyramids, which requires 1.5-1.6 seconds.”
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“This algorithm still achieves excellent performance within each distortion category.”
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“Also, we observe that the performance of the subband at the second finest scale (subband 16) is uniformly very good for all distortion types and on the overall database.”
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“Even for images distorted by Gaussian noise, the performance of the RRED indices is comparable with that of PSNR, which is an FR algorithm.”
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“When the number of scalars required is around 1/40 of the image size, the algorithm achieves a performance which is nearly as good as the best performing full reference QA algorithms.”
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“The performance of the algorithms in the RRED framework has proved to be robust to the choice of the neural noise variance, especially in the regime of high information from the reference.”
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“The outliers in (a), (b) and (c) correspond to images containing a large area of high frequency textured regions.”
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In the paper
“The mean squared error (MSE) has been used as a quality metric for a very long time, owing to its simplicity, despite having a very poor correlation with human perception [1].”
What the sources say
- Not matchedcites [1] [1] Z. Wang and A. C. Bovik, 'Mean squared error: Love it or leave it? - A new look at signal fidelity measures,' IEEE Signal Processing Magazine , vol. 26, no. 1, pp. 98-117, Jan. 2009. -
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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“Of course, since the quality index is based on the absolute difference, it does not indicate which of the two images is the reference image.”
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In the paper
“Moreover, their performances degrade severely with the reduction in the data rate required from the reference.”
What the sources say
- Not checked yetcites [15] [15] X. Gao, W. Lu, D. Tao, and X. Li, 'Image quality assessment based on multiscale geometric analysis,' IEEE Transactions on Image Processing , vol. 18, no. 7, pp. 1409-1423, 2009. - source
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In the paper
“In [11], blind image quality assessment indices that measure the anisotropy in the distorted image through the Renyi entropy are introduced. However, performance of this index has not been thoroughly evaluated on a large and comprehensive dataset.”
What the sources say
- Not checked yetcites [11] [11] S. Gabarda and G. Cristobal, 'Blind image quality assessment through anisotropy,' J. Opt. Soc. Amer. A , vol. 24, pp. B42-B51, 2007. - source
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“Another interesting feature of these algorithms is that they are not dependent on any parameters that need to be trained on databases.”
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In the paper
“Since, the reference information scales with the size of the images, the algorithms are also applicable in scalable image and video QA [21].”
What the sources say
- Not matchedcites [21] [21] K. Seshadrinathan and A. C. Bovik, 'Multi-scale and scalable video quality assessment,' in Proc. IEEE Int Conf on Consumer Electronics , Las Vegas, NV, 2008. -
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In the paper
“This also implies that the RRED indices are always positive.”
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In the paper
“These algorithms depend on parameters that need to be tuned delicately on different databases.”
What the sources say
- Not checked yetcites [15] [15] X. Gao, W. Lu, D. Tao, and X. Li, 'Image quality assessment based on multiscale geometric analysis,' IEEE Transactions on Image Processing , vol. 18, no. 7, pp. 1409-1423, 2009. - source
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“Either image can compute the index using the entropy information from the other image.”
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In the paper
“Our approach to entropic RR QA algorithm design uses conditioning on the realizations of the premultiplier random variables, which is analogous to divisive normalization processes in the primary visual cortex (area V1) of the human visual system.”
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- The authors state this as an assumption: The perceived reference and distorted images pass through an additive neural noise channel, where the noise is a zero mean Gaussian random vector for each block of coefficients.
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In the paper
“Thus the ratio of variances raised to powers is the underlying distortion measure on which a nonlinear logarithmic function is applied.”
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“The results presented below demonstrate that the parameters of the algorithm do not require any training on databases.”
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“Thus it is possible to trade off these performances and achieve a desirable operating point by choosing the corresponding value of σ 2 W .”
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“The reduced performance on the overall database can be attributed to the different ranges of quality scores that occur for different distortion types.”
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“The difference of weighted entropies also ensures numerical stability of the distortions at locations where the energy of the coefficients is extremely small, especially when the neural noise variance is also small.”
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- The authors state this as an assumption: The perceived reference and distorted images pass through an additive neural noise channel, where the noise is a zero mean Gaussian random vector for each block of coefficients.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This suggests that transmitting the right information is crucial to obtain high performance QA algorithms.”
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In the paper
“This is because edge like artifacts introduced by these distortions are reflected better in the coarser subbands.”
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In the paper
“Since (a), (b) and (c) are evaluations of the RRED indices at coarser scales, they do not accurately capture the degradation in quality in these high frequency regions leading to deviations in the logistic fit.”
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“The logarithm operation in the algorithm essentially accomplishes this desirable property.”
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In the paper
“The flattening of the curves from (a) to (d) indicates that the RRED indices at coarser scales tend to cluster the quality indices of most images close to zero.”
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In the paper
“As a result, when weighted entropies are summed up, the gain and loss of entropies tend to cancel each other leading to lower quality ranges.”
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“A distinguishing feature of the RRED indices is that these algorithms do not depend on any parameters that need to be trained on databases.”
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- It may state two separate claims as one. 20
- Probably not a substantial claim. 24
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In the paper
“The algorithms are shown to correlate very well with subjective quality scores as demonstrated on the LIVE Image Quality Assessment Database and Tampere Image Database.”
- Also stated in: § I. INTRODUCTION · p. 4 · boosted
“It is found that the performance attained is highly competitive on a large and comprehensive database of distorted images and subjective scores.”
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It may state two separate claims as one.
- The authors state this as an assumption: The wavelet coefficients of the distorted image can be modeled as a Gaussian scale mixture distribution.
- The authors state this as an assumption: The perceived reference and distorted images pass through an additive neural noise channel, where the noise is a zero mean Gaussian random vector for each block of coefficients.
- Also stated in: § I. INTRODUCTION · p. 4 · boosted
In the paper
“RRED M 16 16 performs better than some of the best full reference algorithms while RRED 1 22 is competitive with PSNR and outperforms [12].”
What the sources say
- Not checked yetcites [12] [12] Z. Wang, G. Wu, H. R. Sheikh, E. P. Simoncelli, E. H. Yang, and A. C. Bovik, 'Quality-aware images,' IEEE Trans. Image Process. , vol. 15, no. 5, pp. 1680-1689, 2006. - source
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In the paper
“The steerable pyramid decomposition of the image has a computational complexity of O ( N log N ) arithmetic operations per scale, where N is the total number of pixels in the image.”
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
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In the paper
“We observe the same trends in Table II as in Table I for SROCC.”
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- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Overall the algorithm requires around 2.8 seconds to transmit the desired information from each (reference or distorted) image.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Finally, computation of the index from the numbers transmitted from the reference and distorted requires time of the order of milliseconds.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The estimation of K U requires O ( N ) operations, while the singular value decomposition of K U requires O ( M 3 ) operations, where K U is of size M × M .”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Similar trends are observed for the other subbands as well.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Further, most of the RRED indices considerably outperform PSNR for all distortion types (except images distorted by Gaussian noise) as well as on the entire database.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The overall performance decays in the subband at the finest scale while the performance in the individual categories is still very good.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The performance of fast fading errors goes down with the fineness of the scale even though the overall performance on the database is still very good.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“However, the algorithms are robust to the exact choice of the size of neighborhoods and we get approximately the same performance for different sizes.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“While the overall performance increases as σ 2 W increases, the performance within the category of images distorted by Gaussian blur decreases.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Observe that even though the overall correlations are reduced by increases in the degree of subsampling, the correlation score for each individual distortion category remains very competitive with state of the art FR algorithms.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The algorithm evaluated in subband 10 yields excellent overall performance (in terms of both SROCC and LCC) as well as for compression, noise and blur distortions.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Further, the estimation of local variance parameters (premultipliers) requires O ( NM 2 ) operations, while sending the desired information from the reference or distorted image can be upper bounded by a cost of O ( N ) .”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“While blur and fast fading errors are better captured by subbands at finer scales, the coarser scales perform better for compressed and noisy images.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Computing the scaled entropies for a subband, which is also the information required to be transmitted takes 0.9-1 seconds for the largest subband.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The algorithm still requires the single number without which quality cannot be computed.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The two methods described above illustrate how the amount of information can be reduced gradually from an almost full reference scenario to an almost reference free scenario.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“RRED 1 k denotes the algorithm in which all the scaled entropy terms in the subband are added and only the sum, which is a single scalar, is required for quality computation.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The above index is a reduced reference index since M k is less than the size of the image.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
- The authors state this as an assumption: The covariance matrices K_U_k and K_V_k are full rank.
In the paper
“The algorithm by [20] based on Weibull statistics of wavelet coefficients achieves good performance at a given data rate.”
What the sources say
- Not checked yetcites [20] [20] W. Xue and X. Mou, 'Reduced reference image quality assessment based on Weibull statistics,' in Second International Workshop on Quality of Multimedia Experience , Trondheim, 2010. - source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“The structural similarity index (SSIM) [2], visual information fidelity (VIF) [3], visual signal to noise ratio (VSNR) [4] and just noticeable difference (JND) metrix [5], are examples of successful full reference algorithms which have been shown to perform well in predicting the quality scores of human subjects.”
What the sources say
- Not matchedcites [2] [2] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, 'Image quality assessment: From error measurement to structural similarity,' IEEE Trans. Image Process. , vol. 13, no. 4, pp. 600-612, Apr. 2004. -
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not checked yetcites [3] [3] H. R. Sheikh and A. C. Bovik, 'Image information and visual quality,' IEEE Trans. Image Process. , vol. 15, no. 2, pp. 430-444, Feb. 2006. - source
- Not checked yetcites [4] [4] D. M. Chandler and S. S. Hemami, 'VSNR: A wavelet-based visual signal-to-noise ratio for natural images,' IEEE Trans. Image Process. , vol. 16, no. 9, pp. 2284-2298, Sep. 2007. - source
boostedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
- Not matched
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“However, we show later on that this procedure still possesses desirable psychovisual properties leading to excellent performance of the algorithms.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The first step in the RR algorithm, similar to IFC/VIF, is a wavelet decomposition of the image at multiple scales and orientations. This step imitates the signal processing that happens in the primary visual cortex (area V1) of the human visual system.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The framework also allows users to choose an algorithm from this class for general purpose or distortion specific quality assessment.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Training based NR QA techniques have resulted in algorithms that perform at least as well as mean squared error, which has the benefit of a reference image [9], [10].”
What the sources say
- Not checked yetcites [9] [9] A. K. Moorthy and A. C. Bovik, 'A two-step framework for constructing blind image quality indices,' IEEE Signal Processing Letters , vol. 17, no. 5, pp. 587-599, May 2010. - source
- Not checked yetcites [10] [10] M. A. Saad, A. C. Bovik, and C. Charrier, 'A DCT statistics based blind image quality index,' IEEE Signal Processing Letters , vol. 17, no. 6, pp. 583-586, Jun. 2010. - source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“However, this algorithm depends on a number of parameters that need to be trained on databases.”
What the sources say
- Not checked yetcites [13] [13] Q. Li and Z. Wang, 'Reduced-reference image quality assessment using divisive normalization-based image representation,' IEEE Journal of Selected Topics in Signal Processing: Special issue on Visual Media Quality Assessment , vol. 3, pp. 202211, 2009. - source
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The performance of this algorithm is good only for certain individual distortion categories.”
What the sources say
- Not checked yetcites [12] [12] Z. Wang, G. Wu, H. R. Sheikh, E. P. Simoncelli, E. H. Yang, and A. C. Bovik, 'Quality-aware images,' IEEE Trans. Image Process. , vol. 15, no. 5, pp. 1680-1689, 2006. - source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Also, any enhanced image would show a difference in entropies and the difference should be interpreted as an improvement in quality.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.
In the paper
“Note that this is the same value of neural noise variance that has been used in prior algorithms [3] and we do not imply any training on the database.”
What the sources say
- Not checked yetcites [3] [3] H. R. Sheikh and A. C. Bovik, 'Image information and visual quality,' IEEE Trans. Image Process. , vol. 15, no. 2, pp. 430-444, Feb. 2006. - source
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“The analysis in [22] suggests that human subjects are more sensitive to horizontal and vertical orientations than others.”
What the sources say
- Not checked yetcites [22] [22] H. R. Sheikh, A. C. Bovik, and G. de Veciana, 'An information fidelity criterion for image quality assessment using natural scene statistics,' IEEE Trans. Image Process. , vol. 14, no. 12, pp. 2117-2128, Dec. 2005. - source
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Therefore, divisive normalization approximates conditioning and vice versa.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- The authors state this as an assumption: The perceived reference and distorted images pass through an additive neural noise channel, where the noise is a zero mean Gaussian random vector for each block of coefficients.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“Note that the reduced reference algorithm operates without knowledge of the distortion type.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“For example, in JPEG, increases in entropy occur due to the introduction of discontinuous blocking artifacts, while decreases in entropy occur in smoother regions that are heavily quantized.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The use of a multiscale multiorientation decomposition before computing the index increases the complexity of the algorithm.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“When the entropies are summed up after the absolute value of the difference is calculated for every block, the changes in the entropies are still preserved leading to an algorithm that possesses better overall performance.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This suggests that the neural noise variance of our model does impact the perception of blur apart from being able to better align scores belonging to different distortion categories.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
The authors state this as an assumption.
Modifications of natural image statistics are perceptually noticeable.
“It is also based on the assumption that such modifications of natural image statistics are perceptually noticeable.”
The authors state this as an assumption.
Non-overlapping blocks of wavelet coefficients are independent and identically distributed.
“Non-overlapping blocks are assumed independent and identically distributed (i.i.d.).”
The authors state this as an assumption.
The wavelet coefficients of the distorted image can be modeled as a Gaussian scale mixture distribution.
“This means that we model the wavelet coefficients of the distorted image as well as a Gaussian scale mixture distribution.”
The authors state this as an assumption.
The perceived reference and distorted images pass through an additive neural noise channel, where the noise is a zero mean Gaussian random vector for each block of coefficients.
“We additionally model the perceived reference and distorted images as passing through an additive neural noise channel, where the noise is assumed to be a zero mean Gaussian random vector for each block of coefficients.”
The authors state this as an assumption.
The covariance matrices K_U_k and K_V_k are full rank.
“In the following, assume that K U k and K V k are full rank matrices.”
The authors state this as an assumption.
The scalar premultiplier S_mk and the Gaussian vector U_mk are independent.
“Also, S mk and ¯ U mk are independent.”
The authors state this as an assumption.
The neural noise vectors W_mk and W'_mk are independent of each other, independent of C_mk and D_mk, and independent across indices m and k.
“where W mk ∼ N (0 , σ 2 W I N ) and W ′ mk ∼ N (0 , σ 2 W I N ) , W mk and W ′ mk are independent of each other, independent of ¯ C mk and ¯ D mk and independent across the indices m and k .”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ V. RESULTS AND DISCUSSION · p. 14
“| Gaussian Blur | 0.9221 | 0.9595 | 0.9678 | 0.9236 | 0.7812 | 0.9728 |”
§ V. RESULTS AND DISCUSSION · p. 16
“| Gaussian Blur | 0.9675 | 0.9429 | 0.9674 | 0.9679 | 0.9655 |”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ V. RESULTS AND DISCUSSION · p. 14
“While blur and fast fading errors are better captured by subbands at finer scales, the coarser scales perform better for compressed and noisy images.”
§ V. RESULTS AND DISCUSSION · p. 14
“The performance of fast fading errors goes down with the fineness of the scale even though the overall performance on the database is still very good.”
Citations
Cites
Image quality assessment: from error visibility to structural similarity
Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.819861 · Cited by 57,892
Self-citationImage information and visual quality
Sheikh, H. R., & Bovik, A. C. (2006) · IEEE Transactions on Image Processing · doi:10.1109/tip.2005.859378 · Cited by 4,104
Self-citationDaugman, J. G. (1985) · Journal of the Optical Society of America A · doi:10.1364/josaa.2.001160 · Cited by 3,219
Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures
Wang, Z., & Bovik, A. C. (2009) · IEEE Signal Processing Magazine · doi:10.1109/msp.2008.930649 · Cited by 3,175
Self-citationImage denoising using scale mixtures of gaussians in the wavelet domain
Portilla, J., Strela, V., Wainwright, M. J., & Simoncelli, E. P. (2003) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.818640 · Cited by 2,280
An information fidelity criterion for image quality assessment using natural scene statistics
Sheikh, H. R., Bovik, A. C., & de Veciana, G. (2005) · IEEE Transactions on Image Processing · doi:10.1109/tip.2005.859389 · Cited by 1,399
Self-citationLive image quality assessment database release 2
Sheikh, H. R. (2005) · Medical Entomology and Zoology · Cited by 1,276
A Two-Step Framework for Constructing Blind Image Quality Indices
Moorthy, A. K., & Bovik, A. C. (2010) · IEEE Signal Processing Letters · doi:10.1109/lsp.2010.2043888 · Cited by 1,196
Self-citationContrast masking in human vision
Legge, G. E., & Foley, J. M. (1980) · Journal of the Optical Society of America · doi:10.1364/josa.70.001458 · Cited by 1,186
VSNR: A Wavelet-Based Visual Signal-to-Noise Ratio for Natural Images
Chandler, D. M., & Hemami, S. S. (2007) · IEEE Transactions on Image Processing · doi:10.1109/tip.2007.901820 · Cited by 1,147
Research works printed but not linked: 1
- 0, JNDmetrix Technology
Cited by
Sorted by citations
No-Reference Image Quality Assessment in the Spatial Domain
Mittal, A., Moorthy, A. K., & Bovik, A. C. (2012) · IEEE Transactions on Image Processing · doi:10.1109/tip.2012.2214050 · Cited by 6,064
Self-citationGradient Magnitude Similarity Deviation: A Highly Efficient Perceptual Image Quality Index
Xue, W., Zhang, L., Mou, X., & Bovik, A. C. (2014) · IEEE Transactions on Image Processing · doi:10.1109/tip.2013.2293423 · Cited by 1,697
Self-citationDeep Neural Networks for No-Reference and Full-Reference Image Quality Assessment
Bosse, S., Maniry, D., Muller, K.-R., Wiegand, T., & Samek, W. (2017) · IEEE Transactions on Image Processing · doi:10.1109/tip.2017.2760518 · Cited by 1,325
Waterloo Exploration Database: New Challenges for Image Quality Assessment Models
Ma, K., Duanmu, Z., Wu, Q., Wang, Z., Yong, H., Li, H., & Zhang, L. (2017) · IEEE Transactions on Image Processing · doi:10.1109/tip.2016.2631888 · Cited by 789
Massive Online Crowdsourced Study of Subjective and Objective Picture Quality
Ghadiyaram, D., & Bovik, A. C. (2016) · IEEE Transactions on Image Processing · doi:10.1109/tip.2015.2500021 · Cited by 782
Self-citation
Metadata
- Authors
- Soundararajan, R., & Bovik, A. C.
- Affiliations
- The University of Texas at Austin (US)
- Venue
- IEEE Transactions on Image Processing
- Published
- 2012-02
- Volume
- 21
- Issue
- 2
- Pages
- 517-526
- ISSN
- 1057-7149 (ISSN-L)
- 1941-0042
- OpenAlex
- W2037243393
- Semantic Scholar
- fa34db4aad1414c88392e0583f5f28c780c7e2e6
- Cited by
- 337
- References
- 38
- Citations by year
- 2026: 5 · 2025: 17 · 2024: 9 · 2023: 14 · 2022: 22 · 2021: 23 · 2020: 21 · 2019: 22 · 2018: 41 · 2017: 36 · 2016: 36 · 2015: 27 · 2014: 33 · 2013: 21 · 2012: 9
- FWCI
- 21.69
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Image Processing (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Video Quality Assessment
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image Retrieval and Classification Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Digital Media Forensic Detection
- Keywords
- reduced-reference image quality assessment, entropy difference, wavelet coefficients, image distortion, visual perception, subjective quality correlation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-09, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-09 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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