Related papers: Quantized Compressed Sensing for Partial Random Ci…
Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the…
Traditionally, quantization is designed to minimize the reconstruction error of a data source. When considering downstream classification tasks, other measures of distortion can be of interest; such as the 0-1 classification loss.…
The recently introduced theory of compressive sensing (CS) enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be…
In this paper, we endeavor for predicting the performance of quantized compressive sensing under the use of sparse reconstruction estimators. We assume that a high rate vector quantizer is used to encode the noisy compressive sensing…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
Recent development in compressed sensing (CS) has revealed that the use of a special design of measurement matrix, namely the spatially-coupled matrix, can achieve the information-theoretic limit of CS. In this paper, we consider the…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
Sparse signals, encountered in many wireless and signal acquisition applications, can be acquired via compressed sensing (CS) to reduce computations and transmissions, crucial for resource-limited devices, e.g., wireless sensors. Since the…
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…
The problem of recovering signals of high complexity from low quality sensing devices is analyzed via a combination of tools from signal processing and harmonic analysis. By using the rich structure offered by the recent development in…
The possible state space dimension increases exponentially with respect to the number of qubits. This feature makes the quantum state tomography expensive and impractical for identifying the state of merely several qubits. The recent…
Quantization of compressed sensing measurements is typically justified by the robust recovery results of Cand\`es, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size $\delta$ is used to quantize…
Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…
In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is the range of a generative neural network (GNN). The problem…
Compressive sensing is a signal processing technique that enables the reconstruction of sparse signals from a limited number of measurements, leveraging the signal's inherent sparsity to facilitate efficient recovery. Recent works on the…
Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a…
This paper provides new error bounds on "consistent" reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from…