MAP recovery of polynomial splines from compressive samples and its application to vehicular signals

Akira Hirabayashi; Satoshi Makido; Laurent Condat

doi:10.1117/12.2024039

26 September 2013 MAP recovery of polynomial splines from compressive samples and its application to vehicular signals

Akira Hirabayashi, Satoshi Makido, Laurent Condat

Proceedings Volume 8858, Wavelets and Sparsity XV; 88580U (2013) https://doi.org/10.1117/12.2024039
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

Abstract

We propose a stable reconstruction method for polynomial splines from compressive samples based on the maximum a posteriori (MAP) estimation. The polynomial splines are one of the most powerful tools for modeling signals in real applications. Since such signals are not band-limited, the classical sampling theorem cannot be applied to them. However, splines can be regarded as signals with finite rate of innovation and therefore be perfectly reconstructed from noiseless samples acquired at, approximately, the rate of innovation. In noisy case, the conventional approach exploits Cadzow denoising. Our approach based on the MAP estimation reconstructs the signals more stably than not only the conventional approach but also a maximum likelihood estimation. We show the effectiveness of the proposed method by applying it to compressive sampling of vehicular signals.

Citation Download Citation

Akira Hirabayashi, Satoshi Makido, and Laurent Condat "MAP recovery of polynomial splines from compressive samples and its application to vehicular signals", Proc. SPIE 8858, Wavelets and Sparsity XV, 88580U (26 September 2013); https://doi.org/10.1117/12.2024039

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