L0-based sparse approximation: two alternative methods and some applications

Javier Portilla; Luis Mancera

doi:10.1117/12.736231

20 September 2007 L0-based sparse approximation: two alternative methods and some applications

Javier Portilla, Luis Mancera

Proceedings Volume 6701, Wavelets XII; 67011Z (2007) https://doi.org/10.1117/12.736231
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

Abstract

We propose two methods for sparse approximation of images under l₂ error metric. First one performs an approximation error minimization given a l_p-norm of the representation through alternated orthogonal projections onto two sets. We study the cases p = 0 (sub-optimal) and p = 1 (optimal), and find that the l₀-AP method is neatly superior, for typical images and overcomplete oriented pyramids. Given that l₁-AP is optimal, this shows that it is not equivalent in practical image processing conditions to minimize one or the other norm, contrarily to what is often assumed. The second method is more powerful, and it performs gradient descent onto decreasingly smoothed versions of the sparse approximation cost function, yielding a method previously proposed as a heuristic. We adapt these techniques for being applied to image restoration, with very positive results.

Citation Download Citation

Javier Portilla and Luis Mancera "L0-based sparse approximation: two alternative methods and some applications", Proc. SPIE 6701, Wavelets XII, 67011Z (20 September 2007); https://doi.org/10.1117/12.736231

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available