Abstract
Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. In this article, we show how sparse coding can be used for denoising. Using maximum likelihood estimation of nongaussian variables corrupted by gaussian noise, we show how to apply a soft-thresholding (shrinkage) operator on the components of sparse coding so as to reduce noise. Our method is closely related to the method of wavelet shrinkage, but it has the important benefit over wavelet methods that the representation is determined solely by the statistical properties of the data. The wavelet representation, on the other hand, relies heavily on certain mathematical properties (like self-similarity) that may be only weakly related to the properties of natural data.
Keywords
WaveletPattern recognition (psychology)Sparse approximationShrinkageThresholdingNoise reductionNeural codingMathematicsArtificial intelligenceRepresentation (politics)AlgorithmComputer scienceStatistics
Related Publications
Image feature extraction by sparse coding and independent component analysis
Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation i...
Image Denoising by Sparse Code Shrinkage
Sparse coding is a method for finding a neural network representation of multidimensional data in which each of the components of the representation is rarely ignorantly active ...
Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising
We develop three novel wavelet domain denoising methods for subband-adaptive, spatially-adaptive and multivalued image denoising. The core of our approach is the estimation of t...
Sparse Representation for Signal Classification
In this paper, application of sparse representation (factorization) of signals over an overcomplete basis (dictionary) for signal classification is discussed.Searching for the s...
Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency
Most simple nonlinear thresholding rules for wavelet-based denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have s...
Publication Info
- Year
- 1999
- Type
- article
- Volume
- 11
- Issue
- 7
- Pages
- 1739-1768
- Citations
- 386
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
386
OpenAlex
Cite This
Aapo Hyvärinen
(1999).
Sparse Code Shrinkage: Denoising of Nongaussian Data by Maximum Likelihood Estimation.
Neural Computation
, 11
(7)
, 1739-1768.
https://doi.org/10.1162/089976699300016214
Identifiers
- DOI
- 10.1162/089976699300016214