Single-pixel compressive imaging based on random DoG filtering

As its name implies, compressive sensing aims to bring compression during sampling. However, the deployment of this technique depends on recovering a high fidelity image through a low number of measurements with a simple hardware and fast software. To this end, we introduce an encoding scheme that by filtering the scene acquires information about the image structure. To prepare a set of proposed encoding patterns, at the first step, a filter bank containing a number of Difference of Gaussian (DoG) kernels with different scales is prepared. Then, by randomly selecting the filters from the bank and under-sampling the scene with them at random points, each encoding pattern is constructed. The idea is inspired by the Human Visual System (HVS) that uses a set of size-tuned DoG kernels at each point in the field-of-view. These encoding patterns, which make a set of linearly independent vectors, form the rows of a structured measurement matrix. This matrix allows making relatively well-conditioned dictionaries by different sparsifying bases. The effectiveness of this method is confirmed by simulations and analyses.