Restoration of intensity and depth images constructed using sparse single-photon data

This paper presents a new algorithm for the joint restoration of depth and intensity images constructed from the time-correlated single-photon counting (TCSPC) measurement in the limit of very few photon counts [1]. Under some justified approximations, the restoration problem (regularized likelihood) reduces to a convex formulation with respect to the parameters of interest. The first advantage of this formulation is that it only processes the corrupted depth and intensity images obtained from preliminary estimation, without the need for the use of full TCSPC waveforms. The second advantage is its flexibility in being able to use different convex regularization terms such as: total variation (TV); and sparsity of the discrete cosine transform (DCT) coefficients. The estimation problems are efficiently solved using the alternating direction method of multipliers (ADMM) that presents good convergence properties and thus a reduced computational cost. Results on single photon depth data from field trials show the benefit of the proposed strategy that improves the quality of the estimated depth and intensity images.