SLOPE: Shrinkage of Local Overlapping Patches Estimator for Lensless Compressive Imaging

A new compressive sensing inversion framework is developed via exploiting the sparsity of local overlapping patches, with the lensless compressive imaging as an exemplar application. This novel framework is formulated to an iteratively two-step process, with the first step projecting the measurements to the data level and the second step aiming to denoise the results obtained in the first step. Under the structure of the sensing matrix used in the hardware, we prove that the proposed algorithm enjoys the anytime property; the algorithm produces a sequence of solutions that monotonically converge to the true signal (thus, anytime). The performance of the proposed algorithm is verified by the real measurements captured by the compressive sensing camera, i.e., the lensless camera, while the algorithm can also be used in other compressive sensing hardware setups. The algorithm is further enhanced by investigating the group sparsity of similar patches in order to improve the performance. Experiments demonstrate that encouraging results are obtained by measuring about 10% (of the image pixels) compressive measurements on both simulation and real datasets.