Stable recovery of analysis based approaches

The theory of compressed sensing shows that it is highly possible to recover a sparse signal from few measurements. Due to its wide applications, compressed sensing has drawn attention of many researchers from the fields of signal and image processing, applied mathematics, and statistics. In this paper we are interested in signals which are sparse under redundant tight frames. Some sufficient conditions are provided to guarantee the stable recovery via solving analysis based approaches. Compared with the previous work [12] and [16], our sufficient conditions are weaker and the estimations of l2l2 bound only depend on the measurement matrix.