Sparse and scale invariant methods in image processing

Abstract : In this thesis, we present new techniques based on the notions of sparsity and scale invariance to design fast and efficient image processing applications. Instead of using the popular l1-norm to model sparsity, we focus on the use of non-convex penalties that promote more sparsity. We propose to use a first-order approximation to estimate a solution of non-convex proximal operators, which permits to easily use a wide range of penalties. We address also the problem of multi-sparsity, when the minimization problem is composed of various sparse terms, which typically arises in problems that require both a robust estimation to reject outliers and a sparse prior. These techniques are applied to various important problems in low-level computer vision such as edgeaware smoothing, image separation, robust integration and image deconvolution. We propose also to go beyond sparsity models and learn non-local spectral mapping with application to image denoising. Scale-invariance is another notion that plays an important role in our work. Using this principle, a precise definition of edges can be derived which can be complementary to sparsity. More precisely, we can extract invariant features for classification from sparse representations in a deep convolutional framework. Scale-invariance permits also to extract relevant pixels for sparsifying images. We use this principle as well to improve optical flow estimation on turbulent images by imposing a sparse regularization on the local singular exponents instead of regular gradients.
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Contributor : H. Yahia <>
Submitted on : Tuesday, December 8, 2015 - 2:54:58 PM
Last modification on : Thursday, May 17, 2018 - 1:11:24 AM
Long-term archiving on: Wednesday, March 9, 2016 - 3:05:39 PM


  • HAL Id : tel-01239958, version 1



Hicham Badri. Sparse and scale invariant methods in image processing. Signal and Image Processing. Université Bordeaux 1 & Université de Rabat, 2015. English. ⟨tel-01239958v1⟩



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