Compressed sensing diffuse optical tomography for molecular and functional brain imaging

Abstract

The optical properties of a highly scattering medium such as tissue can be reconstructed non-invasively by diffuse optical tomography (DOT) based on measurements of scattered and attenuated optical flux. However, due to the diffusive nature of light propagation, the inverse problem of DOT is severely ill-posed and nonlinear. Even though linearized approach or iterative methods that update Green`s function are widely used to reconstruct optical parameters, these approaches suffer from the approximation error or the computational burden of the iterative procedures.

Compressed sensing (CS) is an emerging issue in the field of signal processing, especially multiple measurement vector (MMV) problem in CS considers the recovery of a set of sparse signal vectors that share common non-zero supports, which is called joint sparsity, in the under-determined linear system. Under the condition of the sparsity in the signal and the sufficient incoherency of the sensing matrix, CS enables an accurate recovery even with insufficient number of measurements.

In this dissertation, we developed a novel reconstruction methods for molecular and functional brain imaging in DOT using CS theory. We found that DOT problems in practice can be understood in the framework of the CS, based on the sparse nature of the perturbation in optical properties. Furthermore, the various illumination patterns or temporal information in DOT problem provides the multiple measurement vectors as in MMV problem. Therefore, the original DOT inverse problem can be changed to the joint sparse recovery problem. In other words, the non-linear inverse problem is now changed to the problem of finding the non-zero supports. First, we exploited the joint sparsity in DOT molecular imaging problem and proposed a non-iterative reconstruction algorithm for absorption coefficient and then extended it to simultaneous reconstruction for absorption and scattering coefficients. In functional brain imaging problem, we app...