A novel sparse representation algorithm based on local competitions

In sparse representation, a novel algorithm based on local competitions is proposed to improve the performance of FOCUSS. As l_p optimized function employed in FOCUSS is a non-convex function, FOCUSS has many local minimum, i.e. FOCUSS often can´t get the sparsest solution. To find the sparest representation, a new sparse representation algorithm is proposed, which combines FOCUSS and local competitions. Through implementing competitions between neighboring coefficients in the result of FOCUSS, the new method can overcome the shortcoming of FOCUSS. In the experiment of spectrum estimation, the new algorithm has obtained much better amplitude estimation than FOCUSS. Therefore, the proposed algorithm is an effective sparse representation algorithm.