Tree Structure Based Analyses on Compressive Sensing for Binary Sparse Sources

In this paper we propose a new approach to theoretically analyze compressive sensing directly from the randomly sampling matrix ¿ instead of a certain recovery algorithm. For simplifying our analyses, we consider x as a binary sparse source with independent and identical distribution P¿, where the transform ¿ is omitted as an identity matrix. For convenient analysis, we reform the tree structure in a statistical way to yield a regular tree structure.