Sparse Homogeneous Learning: A New Approach for Sparse Learning

Many sparse representation problems boil down to address the underdetermined systems of linear equations subject to solution sparsity restriction. Many approaches have been proposed such as sparse Bayesian learning. In order to improve solution sparsity and effectiveness in a more intuitive way, a new approach is proposed, which starts from the general solution of the linear equation system. The general solution is decomposed into the particular and homogeneous solutions, where the homogeneous solution is designed to counteract as many elements of particular solution as possible to make the general solution sparse. First, construct a special system of linear equations to link the homogeneous solution with particular solution, which typically is an inconsistent system. Second, the largest consistent sub-system are extracted from the system so that as many corresponding elements of two solutions as possible cancel each other out. By improving implementation efficiency, the procedure can be accomplished with moderate computational time. The results of extensive experiments for sparse signal recovery and image reconstruction demonstrate the superiority of the proposed approach in terms of sparseness or recovery accuracy with acceptable computational burden.