A Greedy Approach to ℓ_0,∞ Based Convolutional Sparse Coding

12/26/2018
by   Elad Plaut, et al.
0

Sparse coding techniques for image processing traditionally rely on a processing of small overlapping patches separately followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used in the processing. For this purpose convolutional sparse coding has been introduced, where a shift-invariant dictionary is used and the sparsity of the recovered image is maintained. Most such strategies target the ℓ_0 "norm" or the ℓ_1 norm of the whole image, which may create an imbalanced sparsity across various regions in the image. In order to face this challenge, the ℓ_0,∞ "norm" has been proposed as an alternative that "operates locally while thinking globally". The approaches taken for tackling the non-convexity of these optimization problems have been either using a convex relaxation or local pursuit algorithms. In this paper, we present an efficient greedy method for sparse coding and dictionary learning, which is specifically tailored to ℓ_0,∞, and is based on matching pursuit. We demonstrate the usage of our approach in salt-and-pepper noise removal and image inpainting. A code package which reproduces the experiments presented in this work is available at https://web.eng.tau.ac.il/ raja

READ FULL TEXT

page 16

page 17

research
05/09/2017

Convolutional Dictionary Learning via Local Processing

Convolutional Sparse Coding (CSC) is an increasingly popular model in th...
research
09/12/2017

Une véritable approche ℓ_0 pour l'apprentissage de dictionnaire

Sparse representation learning has recently gained a great success in si...
research
09/29/2021

Adaptive Approach For Sparse Representations Using The Locally Competitive Algorithm For Audio

Gammachirp filterbank has been used to approximate the cochlea in sparse...
research
09/12/2017

Bridge the Gap Between Group Sparse Coding and Rank Minimization via Adaptive Dictionary Learning

Both sparse coding and rank minimization have led to great successes in ...
research
08/16/2019

Convex geometry of the Coding problem for error constrained Dictionary Learning

In this article we expose the convex geometry of the class of coding pro...
research
11/01/2018

A Local Block Coordinate Descent Algorithm for the Convolutional Sparse Coding Model

The Convolutional Sparse Coding (CSC) model has recently gained consider...
research
10/14/2020

Learned Greedy Method (LGM): A Novel Neural Architecture for Sparse Coding and Beyond

The fields of signal and image processing have been deeply influenced by...

Please sign up or login with your details

Forgot password? Click here to reset