Related papers: Multi-Structural Signal Recovery for Biomedical Co…
The need of reconstructing discrete-valued sparse signals from few measurements, that is solving an undetermined system of linear equations, appears frequently in science and engineering. Whereas classical compressed sensing algorithms do…
Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to…
Magnetic resonance imaging (MRI) is an essential medical tool with inherently slow data acquisition process. Slow acquisition process requires patient to be long time exposed to scanning apparatus. In recent years significant efforts are…
Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or…
Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…
The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
We present a Compressive Sensing algorithm for reconstructing binary signals from its linear measurements. The proposed algorithm minimizes a non-convex cost function expressed as a weighted sum of smoothed $\ell_0$ norms which takes into…
In this paper, we study the issue of estimating a structured signal $x_0 \in \mathbb{R}^n$ from non-linear and noisy Gaussian observations. Supposing that $x_0$ is contained in a certain convex subset $K \subset \mathbb{R}^n$, we prove that…
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…
Compressed sensing takes advantage of low-dimensional signal structure to reduce sampling requirements far below the Nyquist rate. In magnetic resonance imaging (MRI), this often takes the form of sparsity through wavelet transform, finite…
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…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…
Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless…
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…
Emerging sonography techniques often require increasing the number of transducer elements involved in the imaging process. Consequently, larger amounts of data must be acquired and processed. The significant growth in the amounts of data…
The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…
We show that several classical quantities controlling compressed sensing performance directly match classical parameters controlling algorithmic complexity. We first describe linearly convergent restart schemes on first-order methods…
In this work we address the problem of blindly reconstructing compressively sensed signals by exploiting the co-sparse analysis model. In the analysis model it is assumed that a signal multiplied by an analysis operator results in a sparse…
In compressed sensing one uses known structures of otherwise unknown signals to recover them from as few linear observations as possible. The structure comes in form of some compressibility including different notions of sparsity and low…