Image reconstruction from compressive samples via a max-product EM algorithm

Zhao Song; Aleksandar Dogandžić

doi:10.1117/12.930862

15 October 2012 Image reconstruction from compressive samples via a max-product EM algorithm

Zhao Song, Aleksandar Dogandžić

Proceedings Volume 8499, Applications of Digital Image Processing XXXV; 849908 (2012) https://doi.org/10.1117/12.930862
Event: SPIE Optical Engineering + Applications, 2012, San Diego, California, United States

Abstract

We propose a Bayesian expectation-maximization (EM) algorithm for reconstructing structured approximately sparse signals via belief propagation. The measurements follow an underdetermined linear model where the regression-coefficient vector is the sum of an unknown approximately sparse signal and a zero-mean white Gaussian noise with an unknown variance. The signal is composed of large- and small-magnitude components identified by binary state variables whose probabilistic dependence structure is described by a hidden Markov tree (HMT). Gaussian priors are assigned to the signal coefficients given their state variables and the Jeffreys’ noninformative prior is assigned to the noise variance. Our signal reconstruction scheme is based on an EM iteration that aims at maximizing the posterior distribution of the signal and its state variables given the noise variance. We employ a max-product algorithm to implement the maximization (M) step of our EM iteration. The noise variance is a regularization parameter that controls signal sparsity. We select the noise variance so that the corresponding estimated signal and state variables (obtained upon convergence of the EM iteration) have the largest marginal posterior distribution. Our numerical examples show that the proposed algorithm achieves better reconstruction performance compared with the state-of-the-art methods.

Citation Download Citation

Zhao Song and Aleksandar Dogandžić "Image reconstruction from compressive samples via a max-product EM algorithm", Proc. SPIE 8499, Applications of Digital Image Processing XXXV, 849908 (15 October 2012); https://doi.org/10.1117/12.930862

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