Stability of lq-analysis based dual frame with Weibull matrices for 0 < q ≤ 1

Abstract

In practical examples, there are numerous signals that are sparse in a redundant frame rather than an orthonormal basis. This paper mainly focuses on such sparse recovery via [Formula: see text]-analysis-based dual frame with Weibull matrices under the assumption that signals are sparse or compressible in a general frame. First, we give the [Formula: see text] robust null space property and show that it is weaker than the [Formula: see text]-RIP when [Formula: see text] is a general frame. Second, we show that Weibull random matrices with a general dual frame satisfy the [Formula: see text] robust null space property with high probability. Finally, we investigate the stability estimate of [Formula: see text]-analysis based dual frame with Weibull matrices. The result shows that it remains stable and can guarantee accurate recovery of signals with high probability.