Weighted-l1 minimization with multiple weighting sets

Hassan Mansour; Özgür Yilmaz

doi:10.1117/12.894165

27 September 2011 Weighted-ℓ₁ minimization with multiple weighting sets

Hassan Mansour, Özgür Yilmaz

Proceedings Volume 8138, Wavelets and Sparsity XIV; 813809 (2011) https://doi.org/10.1117/12.894165
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

In this paper, we study the support recovery conditions of weighted ℓ₁ minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify a class of signals for which the recovered vector from ℓ₁ minimization provides an accurate support estimate. We then derive stability and robustness guarantees for the weighted ℓ₁ minimization problem with more than one support estimate. We show that applying a smaller weight to support estimate that enjoy higher accuracy improves the recovery conditions compared with the case of a single support estimate and the case with standard, i.e., non-weighted, ℓ₁ minimization. Our theoretical results are supported by numerical simulations on synthetic signals and real audio signals.

Citation Download Citation

Hassan Mansour and Özgür Yilmaz "Weighted-ℓ₁ minimization with multiple weighting sets", Proc. SPIE 8138, Wavelets and Sparsity XIV, 813809 (27 September 2011); https://doi.org/10.1117/12.894165

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