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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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Written from the paper’s full text.
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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In the paper
“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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In the paper
“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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In the paper
“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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In the paper
“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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In the paper
“Table III clearly demonstrates the degradation in the performance of the RR algorithms with subsampling.”
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- 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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“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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“We observe the same trends in Table II as in Table I for SROCC.”
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“Overall the algorithm requires around 2.8 seconds to transmit the desired information from each (reference or distorted) image.”
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“Finally, computation of the index from the numbers transmitted from the reference and distorted requires time of the order of milliseconds.”
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“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 .”
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“Similar trends are observed for the other subbands as well.”
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“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.”
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“The overall performance decays in the subband at the finest scale while the performance in the individual categories is still very good.”
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“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.”
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“However, the algorithms are robust to the exact choice of the size of neighborhoods and we get approximately the same performance for different sizes.”
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“While the overall performance increases as σ 2 W increases, the performance within the category of images distorted by Gaussian blur decreases.”
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“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.”
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“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.”
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“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 ) .”
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“While blur and fast fading errors are better captured by subbands at finer scales, the coarser scales perform better for compressed and noisy images.”
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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.”
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In the paper
“The algorithm still requires the single number without which quality cannot be computed.”
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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.”
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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.”
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In the paper
“The above index is a reduced reference index since M k is less than the size of the image.”
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- 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
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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
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In the paper
“However, we show later on that this procedure still possesses desirable psychovisual properties leading to excellent performance of the algorithms.”
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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.
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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.
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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
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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.
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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
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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.
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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. 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
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Research works printed but not linked: 1
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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).
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