Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm

We present an image reconstruction method for diffuse optical tomography (DOT) by using the sparsity regularization and expectation-maximization (EM) algorithm. Typical image reconstruction approaches in DOT employ Tikhonov-type regularization, which imposes restrictions on the L(2) norm of the optical properties (absorption/scattering coefficients). It tends to cause a blurring effect in the reconstructed image and works best when the unknown parameters follow a Gaussian distribution. In reality, the abnormality is often localized in space. Therefore, the vector corresponding to the change of the optical properties compared with the background would be sparse with only a few elements being nonzero. To incorporate this information and improve the performance, we propose an image reconstruction method by regularizing the L(1) norm of the unknown parameters and solve it iteratively using the expectation-maximization algorithm. We verify our method using simulated 3D examples and compare the reconstruction performance of our approach with the level-set algorithm, Tikhonov regularization, and simultaneous iterative reconstruction technique (SIRT). Numerical results show that our method provides better resolution than the Tikhonov-type regularization and is also efficient in estimating two closely spaced abnormalities.