Related papers: Optimal Compressive Imaging of Fourier Data
Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a…
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…
Modern high-resolution microscopes, such as the scanning tunneling microscope, are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such…
The SPARKLING algorithm was originally developed for accelerated 2D magnetic resonance imaging (MRI) in the compressed sensing (CS) context. It yields non-Cartesian sampling trajectories that jointly fulfill a target sampling density while…
We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain…
In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that…
We introduce an optimal strategy to sample quantum outcomes of local measurement strings for isometric tensor network states. Our method generates samples based on an exact cumulative bounding function, without prior knowledge, in the…
X-ray Computed Tomography (CT) reconstruction from a sparse number of views is a useful way to reduce either the radiation dose or the acquisition time, for example in fixed-gantry CT systems, however this results in an ill-posed inverse…
Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
The primary goal of this work is to review the importance of data compression and present a fast Fourier-based method for generating the deterministic compression matrix in the area of deterministic compressed sensing. The principle…
Undersampling is a common method in Magnetic Resonance Imaging (MRI) to subsample the number of data points in k-space, reducing acquisition times at the cost of decreased image quality. A popular approach is to employ undersampling…
There has been much recent interest in adapting undersampled trajectories in MRI based on training data. In this work, we propose a novel patient-adaptive MRI sampling algorithm based on grouping scans within a training set. Scan-adaptive…
Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking…
Recently Fourier Ptychography (FP) has attracted great attention, due to its marked effectiveness in leveraging snapshot numbers for spatial resolution in large field-of-view imaging. To acquire high signal-to-noise-ratio (SNR) images under…
Purpose: To achieve automatic hyperparameter estimation for the joint recovery of quantitative MR images, we propose a Bayesian formulation of the reconstruction problem that incorporates the signal model. Additionally, we investigate the…
Reconstructing high-quality magnetic resonance images (MRI) from undersampled raw data is of great interest from both technical and clinical point of views. To this date, however, it is still a mathematically and computationally challenging…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…