arXiv subjects

Zhiyong Zhou

Publications and source records attributed to Zhiyong Zhou.

21 records · Page 2Linked to original sources

arXiv2017

Recovery analysis for weighted mixed $\ell_2/\ell_p$ minimization with $0<p\leq 1$

We study the recovery conditions of weighted mixed $\ell_2/\ell_p\,(0<p\leq 1)$ minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. We show that the block $p$-restricted isometry property (RIP) can ensure the robust recovery. Moreover, we present the sufficient and necessary condition for the recovery by using weighted block $p$-null space property. The relationship between the block $p$-RIP and the weighted block $p$-null space property has been established. Finally, we illustrate our results with a series of numerical experiments.

cs.IT↗

arXiv2017

Sparsity estimation in compressive sensing with application to MR images

The theory of compressive sensing (CS) asserts that an unknown signal $\mathbf{x} \in \mathbb{C}^N$ can be accurately recovered from $m$ measurements with $m\ll N$ provided that $\mathbf{x}$ is sparse. Most of the recovery algorithms need the sparsity $s=\lVert\mathbf{x}\rVert_0$ as an input. However, generally $s$ is unknown, and directly estimating the sparsity has been an open problem. In this study, an estimator of sparsity is proposed by using Bayesian hierarchical model. Its statistical properties such as unbiasedness and asymptotic normality are proved. In the simulation study and real data study, magnetic resonance image data is used as input signal, which becomes sparse after sparsified transformation. The results from the simulation study confirm the theoretical properties of the estimator. In practice, the estimate from a real MR image can be used for recovering future MR images under the framework of CS if they are believed to have the same sparsity level after sparsification.

stat.ME↗

arXiv2017

Stable and robust $\ell_p$-constrained compressive sensing recovery via robust width property

We study the recovery results of $\ell_p$-constrained compressive sensing (CS) with $p\geq 1$ via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extends the existing results in Cahill and Mixon (2014) from $\ell_2$-constrained CS to $\ell_p$-constrained case with $p\geq 1$ and complements the recovery analysis for robust CS with $\ell_p$ loss function.

cs.IT↗