Quasi-linear Compressed Sensing

Quasi-linear Compressed Sensing

Inspired by significant real-life applications, in particular, sparse phase retrieval and sparse pulsation frequency detection in Asteroseismology, we investigate a general framework for compressed sensing, where the measurements are quasi-linear. We formulate natural generalizations of the well-known Restricted Isometry Property (RIP) towards nonlinear measurements, which allow us to prove bot...

– Compressed Sensing Linear Algebra Review

One-bit compressed sensing by linear programming

We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x ∈ R from the signs of O(s log(n/s)) random linear measurements of x. The recovery is achieved by a simple linear program. This result extends to approximately sparse vectors x. Our result is universal in the sense that with ...

Linear Array Sar Imaging via Compressed Sensing

In recent years, various attempts have been undertaken to obtain three-dimensional (3-D) reflectivity of observed scene from synthetic aperture radar (SAR) technique. Linear array SAR (LASAR) has been demonstrated as a promising technique to achieve 3-D imaging of earth surface. The common methods used for LASAR imaging are usually based on matched filter (MF) which obeys the traditional Nyquis...

Quasi Gradient Projection Algorithm for Sparse Reconstruction in Compressed Sensing

Compressed sensing is a novel signal sampling theory under the condition that the signal is sparse or compressible. The existing recovery algorithms based on the gradient projection can either need prior knowledge or recovery the signal poorly. In this paper, a new algorithm based on gradient projection is proposed, which is referred as Quasi Gradient Projection. The algorithm presented quasi g...