Software
- Computable performance guarantees for compressed sensing matrices
(Subtitle: How to check the recovery performance of a given sensing matrix in compressed sensing?)
The null space condition for L1 minimization in compressed sensing is a necessary and sufficient condition on the sensing matrices under which a sparse signal can be uniquely recovered from the observation data via L1 minimization. However, verifying the null space condition is known to be computationally challenging. Most of the existing methods can provide only upper and lower bounds on the proportion parameter that characterizes the null space condition. In this paper, we propose new polynomial-time algorithms to establish the upper bounds of the proportion parameter. Based on these polynomial-time algorithms, we have designed new algorithms - Sandwiching Algorithm (SWA) and Tree Search Algorithm (TSA) - to precisely verify the null space condition. Simulation results show that our polynomial- time algorithms can achieve better bounds on recoverable sparsity with low computational complexity than existing methods in the literature. We also show that Tree Search Algorithm and Sandwiching Algorithm significantly reduce the computational complexity when compared with the exhaustive search method.
(Recovery of spectrally sparse signal from partial measurement/ Figuring out frequency locations in the continuous domain from partial time sampled data, or vise versa)
(Finding abnormal random variable out of normal random variable from observations)
(Extracting exact frequency locations in the continuous domain from only partial magnitude observations in the time domain)
(Direction of Arrival (DoA) estimation with auto-sensor calibration)