Name
Title | ||
|---|---|---|
Equivalence probability and sparsity of two sparse solutions in sparse representation. |
Abstract | ||
|---|---|---|
This paper discusses the estimation and numerical calculation of the probability that the 0-norm and 1-norm solutions of underdetermined linear equations are equivalent in the case of sparse representation. First, we define the sparsity degree of a signal. Two equivalence probability estimates are obtained when the entries of the 0-norm solution have different sparsity degrees. One is for the case in which the basis matrix is given or estimated, and the other is for the case in which the basis matrix is random. However, the computational burden to calculate these probabilities increases exponentially as the number of columns of the basis matrix increases. This computational complexity problem can be avoided through a sampling method. Next, we analyze the sparsity degree of mixtures and establish the relationship between the equivalence probability and the sparsity degree of the mixtures. This relationship can be used to analyze the performance of blind source separation (BSS). Furthermore, we extend the equivalence probability estimates to the small noise case. Finally, we illustrate how to use these theoretical results to guarantee a satisfactory performance in underdetermined BSS. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1109/TNN.2008.2003980 | IEEE Transactions on Neural Networks |
Keywords | Field | DocType |
small noise case,basis matrix,basis matrix increase,computational complexity problem,sparsity degree,computational burden,equivalence probability estimate,0-norm solution,different sparsity degree,sparse solutions,equivalence probability,sparse representation,linear equations,computational complexity,noise,probability,signal processing,sparse matrices,blind source separation,sampling methods | Underdetermined system,Matrix (mathematics),Sparse approximation,Equivalence (measure theory),Artificial intelligence,Blind signal separation,Compressed sensing,Sparse matrix,Machine learning,Mathematics,Random matrix | Journal |
Volume | Issue | ISSN |
19 | 12 | 1941-0093 |
Citations | PageRank | References |
14 | 0.75 | 19 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuanqing Li | 1 | 1160 | 97.18 |
| A. Cichocki | 2 | 518 | 40.68 |
| shunichi amari | 3 | 5992 | 1269.68 |
| Shengli Xie | 4 | 2530 | 161.51 |
| C. Guan | 5 | 81 | 3.35 |