Related papers: Robust CS reconstruction based on appropriate mini…
Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…
Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…
From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…
In this paper, we investigate a Bayesian sparse reconstruction algorithm called compressive sensing via Bayesian support detection (CS-BSD). This algorithm is quite robust against measurement noise and achieves the performance of a minimum…
Commonly employed reconstruction algorithms in compressed sensing (CS) use the $L_2$ norm as the metric for the residual error. However, it is well-known that least squares (LS) based estimators are highly sensitive to outliers present in…
Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS…
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…
This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…
We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…
In this paper, we study the problem of robust subspace recovery (RSR) in the presence of both strong adversarial corruptions and Gaussian noise. Specifically, given a limited number of noisy samples -- some of which are tampered by an…
Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy…
Reconstruction fidelity of sparse signals contaminated by sparse noise is considered. Statistical mechanics inspired tools are used to show that the l1-norm based convex optimization algorithm exhibits a phase transition between the…
Compressive sensing (CS) is a signal processing technique that enables sub-Nyquist sampling and near lossless reconstruction of a sparse signal. The technique is particularly appealing for neural signal processing since it avoids the issues…
The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in…
Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further…
The Compressive Sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each…
Magnetic Resonance Imaging (MRI) is one of the most dynamic and safe imaging techniques available for clinical applications. However, the rather slow speed of MRI acquisitions limits the patient throughput and potential indi cations.…
The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which…
Network reconstruction is important to the understanding and control of collective dynamics in complex systems. Most real networks exhibit sparsely connected properties, and the connection parameter is a signal (0 or 1). Well-known…
In ground based infrared imaging a well-known technique to reduce the influence of thermal and background noise is chopping and nodding, where four different signals of the same object are recorded from which the object is reconstructed…