Sparse recovery based compressive sensing algorithms for diffuse optical tomography

Abstract

The optical parameters of a tissue such as a highly turbid medium can be reconstructed by the diffuse optical tomography. It is well known that the inverse problem of DOT is nonlinear, unstable and ill posed due to the propagation of photons through the tissue in a zig-zag manner. Though conventional iterative methods have been employed to solve this problem, they seem to be unsuccessful, considering the complex geometries for study. Recently, the compressive sensing (CS) technique has emerged as recent trend in DOT because of its sparse reconstructions for biomedical applications. The main goal of this paper is to formulate the inverse problem as a single measurement vector (SMV) problem by employing the given CS framework. The greedy algorithms such as compressive sampling matching pursuit (CoSaMP), regularized orthogonal matching pursuit (ROMP), stagewise orthogonal matching pursuit (StOMP), and orthogonal matching pursuit (OMP) are extensively studied to reconstruct the 2D map of the absorption parameter change from the tissue boundary data. The conventional method such as least square technique is studied for comparison. The experimental validation of the greedy algorithms is done on a wax circular phantom through a DOT experimental setup. The performance metrics such as mean square error (MSE), structural similarity index (SSIM), and normalized mean square error (NMSE), are used to assess the performance of the DOT imaging in this paper. The extensive study of the simulation results confirm that the greedy algorithms specially, CoSaMP outperform the conventional methods in DOT.