ABSTRACT
Signals with a large number of elements (big signals or big data) may be characterized by a few nonzero values in one of its representation domains. These signals are called big sparse signals. For reconstruction of such signals, there is no need to sense or store all values. Their reconstruction is possible from a reduced set of linear combinations of its values in the sparsity domain (measurements). The basic definitions of sparse signals and the conditions for their reconstruction are discussed in the first part of this chapter. Many algorithms were developed for the reconstruction of sparse signals. In this chapter, three groups of algorithms are examined. The first group is based on the principle of matching components. The second group of reconstruction algorithms is based on the problem reformulation into a constrained convex form when the linear programming optimization and regression methods can be used. The third one is in obtaining the solution based on the Bayesian approach. The examples of reconstruction using the considered approaches are presented, for their common transformation and measurement/observation matrices.
