Related papers: Compressed Blind De-convolution
In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable…
The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear…
This work addresses the problem of extracting deeply learned features directly from compressive measurements. There has been no work in this area. Existing deep learning tools only give good results when applied on the full signal, that too…
In this work, an efficient numerical scheme is presented for seismic blind deconvolution in a multichannel scenario. The proposed method iterate with wo steps: first, wavelet estimation across all channels and second, refinement of the…
Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently,…
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…
Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…
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…
The hierarchical sparsity framework, and in particular the HiHTP algorithm, has been successfully applied to many relevant communication engineering problems recently, particularly when the signal space is hierarchically structured. In this…
Blind deconvolution is a ubiquitous problem of recovering two unknown signals from their convolution. Unfortunately, this is an ill-posed problem in general. This paper focuses on the {\em short and sparse} blind deconvolution problem,…
Compressed sensing has been a very successful high-dimensional signal acquisition and recovery technique that relies on linear operations. However, the actual measurements of signals have to be quantized before storing or processing.…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a condition, which is independent of the coherence of the tight frame, to guarantee…
Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not…
We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…