Traditionally, compressed sensing assumes a linear, ill-posed or non-invertible forward model, which is inverted with the help of non-convex constraints. Recently these ideas have been extended to non-linear forward models. It could be shown that, under certain conditions, strong performance guarantees available for traditional compressed sensing also hold in the non-linear case. In this paper ...

In Compressed Sensing [9], we consider a signal that is compressible with respect to some dictionary of ’s, that is, its information is concentrated in coefficients . The goal is to reconstruct such signals using only a few measurements , for carefully chosen ’s which depend on . Known results [9], [3], [21] prove that there exists a single measurement matrix such that any compressible signal c...

We consider faithfully combining phase retrieval with classical compressed sensing. Inspired by the recent novel formulation for phase retrieval called PhaseMax, we present and analyze SparsePhaseMax, a linear program for phaseless compressed sensing in the natural parameter space. We establish that when provided with an initialization that correlates with an arbitrary k-sparse n-vector, Sparse...

Compressed sensing is a processing method that significantly reduces the number of measurements needed to accurately resolve signals in many fields of science and engineering. We develop a two-dimensional variant of compressed sensing for multidimensional spectroscopy and apply it to experimental data. For the model system of atomic rubidium vapor, we find that compressed sensing provides an or...

We proposed to apply compressed sensing to realize information sharing of link quality for wireless mesh networks (WMNs) with grid topology. In this paper, we extend the link quality sharing method to be applied for WMNs with arbitrary topology. For arbitrary topology WMNs, we introduce a link quality matrix and a matrix formula for compressed sensing. By employing a diffusion wavelets basis, t...

speckle is a granular disturbance in coherent images such as synthetic aperture radar (sar) images, modeled as a multiplicative noise. this noise degrades the sar image and complicates the image exploitation using automated image analysis techniques. several approaches have been developed to reduce the effect of speckle noise. recently, the application of compressed sensing (cs) is explored in ...

The potential of large tactile arrays to improve robot perception for safe operation in human-dominated environments and of high-resolution tactile arrays to enable humanlevel dexterous manipulation is well accepted. However, the increase in the number of tactile sensing elements introduces challenges including wiring complexity, data acquisition, and data processing. To help address these chal...

As an emerging approach of signal processing, not only has compressed sensing (CS) successfully compressed and sampled signals with few measurements, but also has owned the capabilities of ensuring the exact recovery of signals. However, the above-mentioned properties are based on the (compressed) sensing matrices. Hence the construction of sensing matrices is the key problem. Compared with the...

The restricted isometry property (RIP) has become well-known in the compressed sensing community. Recently, a weaken version of RIP was proposed for exact sparse recovery under weak moment assumptions. In this note, we prove that the weaken RIP is also sufficient for stable and robust sparse recovery by linking it with a recently introduced robust width property in compressed sensing. Moreover,...

Compressed sensing and magnetic resonance imaging are hot topics in the field of signal processing. In this study we introduced in Lustig’s variable density sampling method, integrated it to compressed sensing, and applied it to brain MRI acquisition. The realistic experiment shows the variable density sampling recovery better than traditional random sampling method on a 256x256 brain magnetic ...