There are a large number of methods for solving under-determined linear inverse problems. For large-scale optimization problem, many of them have very high time complexity. We propose a new method called two-stage sparse representation (TSSR) to tackle it. We decompose the representing space of signals into two parts”, the measurement dictionary and the sparsifying basis. The dictionary is designed to obey or nearly obey the sub-Gaussian distribution. The signals are then encoded on the dictionary to obtain the training and testing coefficients individually in the first stage. Then, we design the basis based on the training coefficients to approach an identity matrix, and we apply sparse coding to the testing coefficients over the basis in the second stage. We verify that the projection of testing coefficients onto the basis is a good approximation of the original signals onto the representing space. Since the projection is conducted on a much sparser space, the runtime is greatly reduced. For concrete realization, we provide an instance for the proposed TSSR. Experiments on four biometric databases show that TSSR is effective compared to several classical methods for solving linear inverse problem.
An Efficient Two-Stage Sparse Representation Method