Signal-processing approaches for image-resolution restoration for TOMBO imagery

Thin observation module by bounded optics (TOMBO) is an optical system that achieves compactness and thinness by replacing a conventional large full aperture by a lenslet array with several smaller apertures. This array allows us to collect diverse low-resolution measurements. Finding an efficient way of combining these diverse measurements to make a high-resolution image is an important research problem. We focus on finding a computational method for performing the resolution restoration and evaluating the method via simulations. Our approach is based on advanced signal-processing concepts: we construct a computational data model based on Fourier optics and propose restoration algorithms based on minimization of an information-theoretic measure, called Csiszár's I divergence between two nonnegative quantities: the measured data and the hypothetical images that are induced by our algorithms through the use of our computational data model. We also incorporate Poisson and Gaussian noise processes to model the physical measurements. To solve the optimization problem, we adapt the popular expectation-maximization method. These iterative algorithms, in a multiplicative form, preserve powerful nonnegativity constraints. We further incorporate a regularization based on minimization of total variation to suppress incurring artifacts such as roughness on the surfaces of the estimates. Two sets of simulation examples show that the algorithms can produce very high-quality estimates from noiseless measurements and reasonably good estimates from noisy measurements, even when the measurements are incomplete. Several interesting and useful avenues for future work such as the effects of measurement selection are suggested in our conclusional remarks.