Split Bregman-Singular Value Analysis approach to solve the Compressed Sensing problem of fluorescence diffuse optical tomography

Abstract

Compressed Sensing (CS) techniques are becoming increasingly popular to speed up data acquisition in many modalities. However, most of CS theory is devoted to undetermined problems and there are few contributions that apply it to ill-posed problems. In this work we present a novel approach to CS for fluorescence diffuse optical tomography (fDOT), named the Split Bregman-Singular Value Analysis (SB-SVA) iterative method. This approach is based on the combination of Split Bregman (SB) algorithm to solve CS problems with a theorem about the effect of ill-conditioning on L1 regularization. Our method restricts the solution reached at each SB iteration to a determined space where the singular values of forward matrix and the sparsity structure of each iteration solution combine in a beneficial manner. Taking Battle-Lemarie basis for wavelet transform, where fDOT is sparse, we tested the method with fDOT simulated and experimental data, and found improvement with respect to the results of standard SB algorithm. © Springer International Publishing Sw itzerland 2014.