Novel regularization method for diffuse optical tomography inverse problem

Diffuse optical tomography (DOT) is an optical imaging technique using near-infrared spectroscopy (NIRS). Because the NIR light is highly scattered in biological tissue, the photon density drops rapidly with increasing depth. This makes the measurement accuracy of DOT in deep tissue significantly lower than in superficial tissue. Classical Regularized Least Square (RLS) based regularization methods with different penalty term (l1-norm, l2-norm, LASSO, Ridge, and Elastic Net etc.) come up short in finding the inclusions when the inclusion number is increased or one of the inclusion located on the upper surface and the other one located on the deeper surface of the tissue. This is the depth problem encountered in DOT. In this paper, a new least square based regularization method is proposed. Within the scope of the proposed method, both the weight matrix and penalty terms are modified in order to solve this problem. In this process, firstly, the A matrix is changed using the diagonal value of AAT based on DCA (Depth Compensation Algorithm). Then, a new penalty term using modified A matrix is added. It has been observed that when the noise level increases, proposed method give higher accuracy and more robust according to other RLS Method on synthetic data. Experimental results on synthetic data show that the new method improves inversion accuracy, reduces errors, and the lowers inversion instability compared to the state-of-the-art methods.