Related papers: Robust Dequantized Compressive Sensing
We consider the problem of calibrating a compressed sensing measurement system under the assumption that the decalibration consists in unknown gains on each measure. We focus on {\em blind} calibration, using measures performed on a few…
We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…
Conventional compressed sensing theory assumes signals have sparse representations in a known, finite dictionary. Nevertheless, in many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the…
A novel framework to construct an efficient sensing (measurement) matrix, called mixed adaptive-random (MAR) matrix, is introduced for directly acquiring a compressed image representation. The mixed sampling (sensing) procedure hybridizes…
We show that measures with finite support on the real line are the unique solution to an algorithm, named generalized minimal extrapolation, involving only a finite number of generalized moments (which encompass the standard moments, the…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
This work theoretically studies the problem of estimating a structured high-dimensional signal $x_0 \in \mathbb{R}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge…
Compressed Sensing (CS) is an effective approach to reduce the required number of samples for reconstructing a sparse signal in an a priori basis, but may suffer severely from the issue of basis mismatch. In this paper we study the problem…
Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…
We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. When such a signal is acquired according to the principles of CS, the measurements still…
Corrupted sensing concerns the problem of recovering a high-dimensional structured signal from a collection of measurements that are contaminated by unknown structured corruption and unstructured noise. In the case of linear measurements,…
The goal of compressed sensing is to learn a structured signal $x$ from a limited number of noisy linear measurements $y \approx Ax$. In traditional compressed sensing, "structure" is represented by sparsity in some known basis. Inspired by…
Numerous applications in signal processing have benefited from the theory of compressed sensing which shows that it is possible to reconstruct signals sampled below the Nyquist rate when certain conditions are satisfied. One of these…
Long-range correlated errors can severely impact the performance of NISQ (noisy intermediate-scale quantum) devices, and fault-tolerant quantum computation. Characterizing these errors is important for improving the performance of these…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
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…
This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension. We provide a convex recovery…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…