Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
SUSAN—A New Approach to Low Level Image Processing
International Journal of Computer Vision
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Handbook of Image and Video Processing
Handbook of Image and Video Processing
Reconstruction of Wavelet Coefficients Using Total Variation Minimization
SIAM Journal on Scientific Computing
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Extensions of compressed sensing
Signal Processing - Sparse approximations in signal and image processing
Nonlocal Image and Movie Denoising
International Journal of Computer Vision
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
SIAM Journal on Optimization
Robust recovery of signals from a structured union of subspaces
IEEE Transactions on Information Theory
Model-based compressive sensing
IEEE Transactions on Information Theory
A robust and fast non-local means algorithm for image denoising
Journal of Computer Science and Technology
Embedded image coding using zerotrees of wavelet coefficients
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
IEEE Transactions on Image Processing
Skellam Shrinkage: Wavelet-Based Intensity Estimation for Inhomogeneous Poisson Data
IEEE Transactions on Information Theory
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Image denoising is an important issue in many real applications. Image denoising can be considered to be recovering a signal from inaccurately and/or partially measured samples, which is exactly what compressive sensing accomplishes. With this observation, we propose a general image denoising framework that is based on compressive sensing theory in this paper. Most wavelet-based and total variation based image denoising algorithms can be considered to be special cases of our framework. From the perspective of compressive sensing theory, these algorithms can be improved. To demonstrate such an improvement, we devise four novel algorithms that are specialized from our framework. The first algorithm, which is for the synthetic case, demonstrates the considerable potential of our framework. The second algorithm, which is an extension of wavelet thresholding and total variation regularization, has better performance on natural image denoising than these algorithms. The third algorithm is a more sophisticated algorithm for natural image with Gaussian white noise. The last algorithm addresses Poisson-corrupted images. Compared with several state-of-the-art algorithms, our intensive experiments show that our method has a good performance in PSNR (peak signal-to-noise ratio), fewer artifacts and high quality with respect to visual checking.