Sparse Approximation of Images Inspired from the Functional Architecture of the Primary Visual Areas

Sylvain Fischer,Laurent Perrinet,Rafael Redondo,Gabriel Cristóbal

doi:10.1155/2007/90727

Abstract

Several drawbacks of critically sampled wavelets can be solved by overcomplete multiresolution transforms and sparse approximation algorithms. Facing the difficulty to optimize such nonorthogonal and nonlinear transforms, we implement a sparse approximation scheme inspired from the functional architecture of the primary visual cortex. The scheme models simple and complex cell receptive fields through log-Gabor wavelets. The model also incorporates inhibition and facilitation interactions between neighboring cells. Functionally these interactions allow to extract edges and ridges, providing an edge-based approximation of the visual information. The edge coefficients are shown sufficient for closely reconstructing the images, while contour representations by means of chains of edges reduce the information redundancy for approaching image compression. Additionally, the ability to segregate the edges from the noise is employed for image restoration.

Highlights

Recent works on multiresolution transforms showed the necessity of using overcomplete transformations to solve drawbacks oforthogonal wavelets, namely their lack of shift invariance, the aliasing between subbands, their poor resolution in orientation and their insufficient match with image features [1,2,3,4]
We propose here to build a new method for sparse approximation of natural images based both on classical image processing criteria and on the known physiology of the primary visual cortex (V1) of primates
We propose here a unified algorithm for denoising, edge extraction, and image compression based on a new sparse approximation strategy for natural images

Summary

Introduction

Recent works on multiresolution transforms showed the necessity of using overcomplete transformations to solve drawbacks of (bi-)orthogonal wavelets, namely their lack of shift invariance, the aliasing between subbands, their poor resolution in orientation and their insufficient match with image features [1,2,3,4]. Two main classes of algorithms are available: matching pursuit (MP) [5, 10] which recursively chooses the most relevant coefficients in all the dictionary and basis pursuit (BP) [6] which minimizes a penalizing function corresponding to the sum of the amplitude of all coefficients. Both these algorithms perform iteratively and globally through all the dictionary. They are computationally costly algorithms which generally only achieve approximations of the optimal solutions

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Conclusion