Related papers: Compressed sensing for inverse problems and the sa…
Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from…
We consider the problem of spectral compressed sensing in continuous domain, which aims to recover a 2-dimensional spectrally sparse signal from partially observed time samples. The signal is assumed to be a superposition of s complex…
We present improved sampling complexity bounds for stable and robust sparse recovery in compressed sensing. Our unified analysis based on l1 minimization encompasses the case where (i) the measurements are block-structured samples in order…
Compressive sensing relies on the sparse prior imposed on the signal of interest to solve the ill-posed recovery problem in an under-determined linear system. The objective function used to enforce the sparse prior information should be…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…
Wideband spectrum sensing detects the unused spectrum holes for dynamic spectrum access (DSA). Too high sampling rate is the main problem. Compressive sensing (CS) can reconstruct sparse signal with much fewer randomized samples than…
Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…
To obtain the best resolution for any measurement there is an ever-present challenge to achieve maximal differentiation between signal and noise over as fine of sampling dimensions as possible. In diffraction science these issues are…
Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown significant…
Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…
This chapter gives an overview over recovery guarantees for total variation minimization in compressed sensing for different measurement scenarios. In addition to summarizing the results in the area, we illustrate why an approach that is…
Numerous applications in signal processing have benefited from the theory of compressed sensing which shows that it is possible to reconstruct signals sampled below the Nyquist rate when certain conditions are satisfied. One of these…
The reconstruction of three-dimensional sparse volume functions from few tomographic projections constitutes a challenging problem in image reconstruction and turns out to be a particular instance problem of compressive sensing. The…
In this paper, the theoretical analysis of compressive sensing via random filter, firstly outlined by J. Romberg [compressive sensing by random convolution, submitted to SIAM Journal on Imaging Science on July 9, 2008], has been refined or…
Compressive Sensing theory says that it is possible to reconstruct a measured signal if an enough sparse representation of this signal exists in comparison to the number of random measurements. This theory was applied to reconstruct signals…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
Due to the many applications in Magnetic Resonance Imaging (MRI), Nuclear Magnetic Resonance (NMR), radio interferometry, helium atom scattering etc., the theory of compressed sensing with Fourier transform measurements has reached a mature…
Compressive sensing is a novel approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate and outperforms traditional signal processing techniques in acquiring and reconstructing…
We study the use of very sparse random projections for compressed sensing (sparse signal recovery) when the signal entries can be either positive or negative. In our setting, the entries of a Gaussian design matrix are randomly sparsified…