Gram-Guided Error-Correction for Highly-Coherent Dictionaries and its Application to CS-ToF Imaging

During the design of any demodulation scheme in Compressive Sensing-based Time-of-Flight, we face two opposing criteria. On the one hand, we aim to minimize the number of measurements and, thus, the number of rows of the sensing matrix, to reduce acquisition times and approach real-time operation. On the other hand, we would like to recover the target's depth in a grid as fine as possible to enhance the depth resolution. In this scenario, the sensing matrices become fat and their coherence close to the unit. In this paper, we present an original error-correction method to prevent from the appearance of depth estimation errors derived from this effect. Our algorithm first identifies the most correlated columns in the sensing matrix and then exploits the recovered depths over a pixel neighborhood to determine the most recommendable correction. Without loss of generality, we add this step to each iteration of Orthogonal Matching Pursuit and evaluate the performance gain.