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Accurate measurement of spatially variant noise in dynamic magnetic resonance (MR) images acquired using parallel imaging methods is problematic. We propose a new method based on the random matrix theory to accurately assess the noise…
We make use of recent results from random matrix theory to identify a derived threshold, for isolating noise from image features. The procedure assumes the existence of a set of noisy images, where denoising can be carried out on individual…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Dimensionality reduction (DR) of image features plays an important role in image retrieval and classification tasks. Recently, two types of methods have been proposed to improve the both the accuracy and efficiency for the dimensionality…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
Cardiac cine magnetic resonance imaging (MRI) can be considered the optimal criterion for measuring cardiac function. This imaging technique can provide us with detailed information about cardiac structure, tissue composition and even blood…
We present new, original and alternative method for searching signals coded in noisy data. The method is based on the properties of random matrix eigenvalue spectra. First, we describe general ideas and support them with results of…
Computing accurate low rank approximations of large matrices is a fundamental data mining task. In many applications however the matrix contains sensitive information about individuals. In such case we would like to release a low rank…
In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
Large high-dimensional datasets are becoming more and more popular in an increasing number of research areas. Processing the high dimensional data incurs a high computational cost and is inherently inefficient since many of the values that…
Recovering a low-rank signal matrix from its noisy observation, commonly known as matrix denoising, is a fundamental inverse problem in statistical signal processing. Matrix denoising methods are generally based on shrinkage or thresholding…
In the realm of cardiovascular medicine, medical imaging plays a crucial role in accurately classifying cardiac diseases and making precise diagnoses. However, the field faces significant challenges when integrating data science techniques,…
The crucial components of a conventional image registration method are the choice of the right feature representations and similarity measures. These two components, although elaborately designed, are somewhat handcrafted using human…
This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\mathbf{M}^{\star}\in \mathbb{R}^{n\times n}$, yet only a randomly…
This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…
Population imaging studies rely upon good quality medical imagery before downstream image quantification. This study provides an automated approach to assess image quality from cardiovascular magnetic resonance (CMR) imaging at scale. We…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast between two biological matters on the pictures. Geometric…