Related papers: How to get high resolution results from sparse and…

1-bit compressive sensing aims to recover sparse signals from quantized 1-bit measurements. Designing efficient approaches that could handle noisy 1-bit measurements is important in a variety of applications. In this paper we use the…

This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal…

Conventional approaches of sampling signals follow the celebrated theorem of Nyquist and Shannon. Compressive sampling, introduced by Donoho, Romberg and Tao, is a new paradigm that goes against the conventional methods in data acquisition…

In this paper, we consider compressive sensing (CS)-based recovery of delays and Doppler frequencies of targets in high resolution radars. We propose a novel sub-Nyquist sampling method in the Fourier domain based on difference sets (DS),…

Non-regular sampling can reduce aliasing at the expense of noise. Recently, it has been shown that non-regular sampling can be carried out using a conventional regular imaging sensor when the surface of its individual pixels is partially…

Super-resolution is generally referred to as the task of recovering fine details from coarse information. Motivated by applications such as single-molecule imaging, radar imaging, etc., we consider parameter estimation of complex…

Network reconstruction of dynamical continuous-time (CT) systems is motivated by applications in many fields. Due to experimental limitations, especially in biology, data could be sampled at low frequencies, leading to significant…

We introduce a new audio processing technique that increases the sampling rate of signals such as speech or music using deep convolutional neural networks. Our model is trained on pairs of low and high-quality audio examples; at test-time,…

The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…

This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…

Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…

This note addresses identification of the $A$-matrix in continuous time linear dynamical systems on state-space form. If this matrix is partially known or known to have a sparse structure, such knowledge can be used to simplify the…

Avoiding aliasing in time-resolved flow data obtained through high fidelity simulations while keeping the computational and storage costs at acceptable levels is often a challenge. Well-established solutions such as increasing the sampling…

In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis to decompose the signal is not…

Most image super-resolution (SR) methods are developed on synthetic low-resolution (LR) and high-resolution (HR) image pairs that are constructed by a predetermined operation, e.g., bicubic downsampling. As existing methods typically learn…

We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is…

The primary aim of single-image super-resolution is to construct high-resolution (HR) images from corresponding low-resolution (LR) inputs. In previous approaches, which have generally been supervised, the training objective typically…

The article considers the problem of estimating a high-dimensional sparse parameter in the presence of side information that encodes the sparsity structure. We develop a general framework that involves first using an auxiliary sequence to…

This paper studies a spectrum estimation method for the case that the samples are obtained at a rate lower than the Nyquist rate. The method is referred to as the correlogram for undersampled data. The algorithm partitions the spectrum into…

Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…