Split Bregman-Singular Value Analysis Approach to Solve the Compressed Sensing Problem of Fluorescence Diffuse Optical Tomography

Compressed Sensing (CS) techniques are becom- ing increasingly popular to speed up data acquisition in many modalities. However, most of CS theory is devoted to undeter- mined problems and there are few contributions that apply it to ill-posed problems. In this work we present a novel ap- proach 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 expe- rimental data, and found improvement with respect to the results of standard SB algorithm.