Seismic Denoising with Nonuniformly Sampled Curvelets
Computing in Science and Engineering
Sparse coding via thresholding and local competition in neural circuits
Neural Computation
Flexible Component Analysis for Sparse, Smooth, Nonnegative Coding or Representation
Neural Information Processing
Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
A Predual Proximal Point Algorithm Solving a Non Negative Basis Pursuit Denoising Model
International Journal of Computer Vision
A fast approach for overcomplete sparse decomposition based on smoothed l0 norm
IEEE Transactions on Signal Processing
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
IEEE Transactions on Image Processing
A fast multilevel algorithm for wavelet-regularized image restoration
IEEE Transactions on Image Processing
From Local Kernel to Nonlocal Multiple-Model Image Denoising
International Journal of Computer Vision
A subband adaptive iterative shrinkage/thresholding algorithm
IEEE Transactions on Signal Processing
Double sparsity: learning sparse dictionaries for sparse signal approximation
IEEE Transactions on Signal Processing
Deconvolution of poissonian images via iterative shrinkage
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
IEEE Transactions on Signal Processing
On the stable recovery of the sparsest overcomplete representations in presence of noise
IEEE Transactions on Signal Processing
A shrinkage learning approach for single image super-resolution with overcomplete representations
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Exact optimization for the l1-Compressive Sensing problem using a modified Dantzig-Wolfe method
Theoretical Computer Science
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A novel predual dictionary learning algorithm
Journal of Visual Communication and Image Representation
Analysis and Generalizations of the Linearized Bregman Method
SIAM Journal on Imaging Sciences
Alternating Direction Algorithms for $\ell_1$-Problems in Compressive Sensing
SIAM Journal on Scientific Computing
Alternating Direction Method for Image Inpainting in Wavelet Domains
SIAM Journal on Imaging Sciences
Efficient minimization for dictionary based sparse representation and signal recovery
Proceedings of the 4th International Symposium on Applied Sciences in Biomedical and Communication Technologies
A Simple Compressive Sensing Algorithm for Parallel Many-Core Architectures
Journal of Signal Processing Systems
Learned shrinkage approach for low-dose reconstruction in computed tomography
Journal of Biomedical Imaging
Hi-index | 754.86 |
Shrinkage is a well known and appealing denoising technique, introduced originally by Donoho and Johnstone in 1994. The use of shrinkage for denoising is known to be optimal for Gaussian white noise, provided that the sparsity on the signal's representation is enforced using a unitary transform. Still, shrinkage is also practiced with nonunitary, and even redundant representations, typically leading to very satisfactory results. In this correspondence we shed some light on this behavior. The main argument in this work is that such simple shrinkage could be interpreted as the first iteration of an algorithm that solves the basis pursuit denoising (BPDN) problem. While the desired solution of BPDN is hard to obtain in general, we develop a simple iterative procedure for the BPDN minimization that amounts to stepwise shrinkage. We demonstrate how the simple shrinkage emerges as the first iteration of this novel algorithm. Furthermore, we show how shrinkage can be iterated, turning into an effective algorithm that minimizes the BPDN via simple shrinkage steps, in order to further strengthen the denoising effect