PAT image reconstruction using augmented sparsity regularization with semi-automated tuning of regularization weight

Among all tissue imaging modalities, photo-acoustic tomography (PAT) has been getting increasing attention in the recent past due to the fact that it has high contrast, high penetrability, and has capability of retrieving high resolution. The reconstruction methods used in PAT plays a crucial role in the applicability of PAT, and PAT finds particularly a wider applicability if a model-based regularized reconstruction method is used. A crucial factor that determines the quality of reconstruction in such methods is the choice of regularization weight. Unfortunately, an appropriately tuned value of regularization weight varies significantly with variation in the noise level, as well as, with the variation in the high resolution contents of the image, in a way that has not been well understood. There has been attempts to determine optimum regularization weight from the measured data in the context of using elementary and general purpose regularizations. In this paper, we develop a method for semi-automated tuning of the regularization weight in the context of using a modern type of regularization that was specifically designed for PAT image reconstruction. As a first step, we introduce a relative smoothness constraint with a parameter; this parameter computationally maps into the actual regularization weight, but, its tuning does not vary significantly with variation in the noise level, and with the variation in the high resolution contents of the image. Next, we construct an algorithm that integrates the task of determining this mapping along with obtaining the reconstruction. Finally we demonstrate experimentally that we can run this algorithm with a nominal value of the relative smoothness parameter -- a value independent of the noise level and the structure of the underlying image -- to obtain good quality reconstructions.