Related papers: Learning to Sample: Data-Driven Sampling and Recon…
The paper considers the problem of identifying the sparse different components between two high dimensional means of column-wise dependent random vectors. We show that the dependence can be utilized to lower the identification boundary for…
An architecture for hardware realization of a system for sparse signal reconstruction is presented. The threshold based reconstruction method is considered, which is further modified in this paper to reduce the system complexity in order to…
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…
This paper focuses on detection tasks in information extraction, where positive instances are sparsely distributed and models are usually evaluated using F-measure on positive classes. These characteristics often result in deficient…
Compressed sensing (CS) MRI relies on adequate undersampling of the k-space to accelerate the acquisition without compromising image quality. Consequently, the design of optimal sampling patterns for these k-space coefficients has received…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
The ability of a radar to discriminate in both range and Doppler velocity is completely characterized by the ambiguity function (AF) of its transmit waveform. Mathematically, it is obtained by correlating the waveform with its…
We consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of…
Greedy Pursuits are very popular in Compressed Sensing for sparse signal recovery. Though many of the Greedy Pursuits possess elegant theoretical guarantees for performance, it is well known that their performance depends on the statistical…
Recently, score-based diffusion models have shown satisfactory performance in MRI reconstruction. Most of these methods require a large amount of fully sampled MRI data as a training set, which, sometimes, is difficult to acquire in…
Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors…
We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection. By…
In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…
We study the problem of interpolating a noisy Fourier-sparse signal in the time duration $[0, T]$ from noisy samples in the same range, where the ground truth signal can be any $k$-Fourier-sparse signal with band-limit $[-F, F]$. Our main…
Accurate BRDF acquisition is essential for realistic rendering, but dense gonioreflectometer measurements are slow and expensive. We study how to select a small set of BRDF measurements that is most informative for reconstructing material…
Depth acquisition, based on active illumination, is essential for autonomous and robotic navigation. LiDARs (Light Detection And Ranging) with mechanical, fixed, sampling templates are commonly used in today's autonomous vehicles. An…
There is much recent interest in techniques to accelerate the data acquisition process in MRI by acquiring limited measurements. Often sophisticated reconstruction algorithms are deployed to maintain high image quality in such settings. In…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…