相关论文: Minimum Complexity Pursuit for Universal Compresse…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
Compressed sensing is a new data acquisition paradigm enabling universal, simple, and reduced-cost acquisition, by exploiting a sparse signal model. Most notably, recovery of the signal by computationally efficient algorithms is guaranteed…
The paper studies the problem of recovering a spectrally sparse object from a small number of time domain samples. Specifically, the object of interest with ambient dimension $n$ is assumed to be a mixture of $r$ complex multi-dimensional…
In this paper, we propose an algorithm referred to as multipath matching pursuit that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to…
Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to…
Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…
We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…
Recently, many practical algorithms have been proposed to recover the sparse signal from fewer measurements. Orthogonal matching pursuit (OMP) is one of the most effective algorithm. In this paper, we use the restricted isometry property to…
Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…
In this paper, the problem of developing universal algorithms for compressed sensing of stochastic processes is studied. First, R\'enyi's notion of information dimension (ID) is generalized to analog stationary processes. This provides a…
In this paper, we bring together two trends that have recently emerged in sparse signal recovery: the problem of sparse signals that stem from finite alphabets and the techniques that introduce concave penalties. Specifically, we show that…
In many applications we seek to recover signals from linear measurements far fewer than the ambient dimension, given the signals have exploitable structures such as sparse vectors or low rank matrices. In this paper we work in a general…
Compressed sensing is triggering a major evolution in signal acquisition. It consists in sampling a sparse signal at low rate and later using computational power for its exact reconstruction, so that only the necessary information is…
It has been found that radar returns of extended targets are not only sparse but also exhibit a tendency to cluster into randomly located, variable sized groups. However, the standard techniques of Compressive Sensing as applied in radar…
In compressed sensing, one wishes to acquire an approximately sparse high-dimensional signal $x\in\mathbb{R}^n$ via $m\ll n$ noisy linear measurements, then later approximately recover $x$ given only those measurement outcomes. Various…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
Orthogonal matching pursuit (OMP) is a greedy algorithm widely used for the recovery of sparse signals from compressed measurements. In this paper, we analyze the number of iterations required for the OMP algorithm to perform exact recovery…