This paper deals with the problem of depth recovery and image restoration from sparse and noisy image data. The image is modeled as a Markov random field and a new energy function is developed to effectively detect discontinuities in highly sparse and noisy images. The model provides an alternative to the use of a line process. Interpolation over missing data sites is first done using local characteristics to obtain initial estimates and then simulated annealing is used to compute the maximum a posteriori (MAP) estimate. A threshold on energy reduction per iteration is used to speed up simulated annealing by avoiding computation that contributes little to the energy minimization. Moreover, a minor modification of the posterior energy function gives improved results for random as well as structured sparsing problems. Results of simulations carried out on real range and intensity images along with details of the simulations are presented.
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