Related papers: One Scan 1-Bit Compressed Sensing
We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
This paper provides a unified treatment to the recovery of structured signals living in a star-shaped set from general quantized measurements $\mathcal{Q}(\mathbf{A}\mathbf{x}-\mathbf{\tau})$, where $\mathbf{A}$ is a sensing matrix,…
We investigate the sign-linear embeddings of 1-bit compressed sensing given by Gaussian measurements. One can give short arguments concerning a Restricted Isometry Property of such maps using Vapnik-Chervonenkis dimension of sparse…
This letter proposes a low-computational Bayesian algorithm for noisy sparse recovery in the context of one bit compressed sensing with sensing matrix perturbation. The proposed algorithm which is called BHT-MLE comprises a sparse support…
The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.…
Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any $n$-dimensional vector that is $k$-sparse (with $k\ll n$) can be fully recovered using…
Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random…
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…
In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of…
Compressed sensing is a signal processing scheme that reconstructs high-dimensional sparse signals from a limited number of observations. In recent years, various problems involving signals with a finite number of discrete values have been…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…
This paper studies the stability of some reconstruction algorithms for compressed sensing in terms of the bit precision. Considering the fact that practical digital systems deal with discretized signals, we motivate the importance of the…
Compressed sensing (CS) demonstrates that a sparse, or compressible signal can be acquired using a low rate acquisition process below the Nyquist rate, which projects the signal onto a small set of vectors incoherent with the sparsity…
Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
We propose a distributed algorithm for sparse signal recovery in sensor networks based on Iterative Hard Thresholding (IHT). Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their…
Sparse signal recovery or compressed sensing can be formulated as certain sparse optimization problems. The classic optimization theory indicates that the Newton-like method often has a numerical advantage over the gradient method for…