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Interpolation revisited [medical images application]
Open accessAbstract
Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are not interpolating. By opposition to traditional interpolation, we call their use generalized interpolation; they involve a prefiltering step when correctly applied. We explain why the approximation order inherent in any basis function is important to limit interpolation artifacts. The decomposition theorem states that any basis function endowed with approximation order can be expressed as the convolution of a B-spline of the same order with another function that has none. This motivates the use of splines and spline-based functions as a tunable way to keep artifacts in check without any significant cost penalty. We discuss implementation and performance issues, and we provide experimental evidence to support our claims.
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Cited by
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Ashburner, J. (2007) · NeuroImage · doi:10.1016/j.neuroimage.2007.07.007 · Cited by 8,122
Ashburner, J., & Friston, K. J. (2005) · NeuroImage · doi:10.1016/j.neuroimage.2005.02.018 · Cited by 7,507
Image registration methods: a survey
Zitová, B., & Flusser, J. (2003) · Image and Vision Computing · doi:10.1016/s0262-8856(03)00137-9 · Cited by 6,423
Elastix: a toolbox for intensity-based medical image registration
Klein, S., Staring, M., Murphy, K., Viergever, M. A., & Pluim, J. (2010) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2009.2035616 · Cited by 4,311
Deep Convolutional Neural Network for Inverse Problems in Imaging
Jin, K. H., McCann, M. T., Froustey, E., & Unser, M. (2017) · IEEE Transactions on Image Processing · doi:10.1109/tip.2017.2713099 · Cited by 2,529
“Over the past decades, iterative reconstruction methods have become the dominant approach to solving inverse problems in imaging including denoising [1]–[4], deconvolution [5], [6], and interpolation [7], [8]. Thanks to robust regularizers such as total variation [1], [2], [5] and sparsity [9], practical algorithms ha…”
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Metadata
- Authors
- Thevenaz, P., Blu, T., & Unser, M.
- Venue
- IEEE Transactions on Medical Imaging
- Published
- 2000-07
- Volume
- 19
- Issue
- 7
- Pages
- 739-758
- ISSN
- 0278-0062 (ISSN-L)
- OpenAlex
- W2065628492
- Cited by
- 842
- References
- 0
- FWCI
- 21.48
- Type
- journal article
- Language
- en
- Open access
- green
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- Thevenaz, P., Blu, T., & Unser, M. (2000). Interpolation revisited [medical images application]. IEEE Transactions on Medical Imaging. https://doi.org/10.1109/42.875199
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