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Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…
We study the problem of exact completion for $m \times n$ sized matrix of rank $r$ with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call…
We study the shape of convective rolls in the Marine Atmospheric Boundary Layer from Synthetic Aperture Radar images of the ocean. We propose a multiscale analysis with structure functions which allow an easy generalization to analyse…
Optimized sensing is important for computational imaging in low-resource environments, when images must be recovered from severely limited measurements. In this paper, we propose a physics-constrained, fully differentiable, autoencoder that…
Compressed sensing theory indicates that selecting a few measurements independently at random is a near optimal strategy to sense sparse or compressible signals. This is infeasible in practice for many acquisition devices that acquire…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…
Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…
The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…
Magnetic Resonance Imaging (MRI) is a kind of medical imaging technology used for diagnostic imaging of diseases, but its image quality may be suffered by the long acquisition time. The compressive sensing (CS) based strategy may decrease…
This paper explores an energy-modified leverage sampling strategy for matrix completion in radio map construction. The main goal is to address potential identifiability issues in matrix completion with sparse observations by using a…
Undersampling the k-space during MR acquisitions saves time, however results in an ill-posed inversion problem, leading to an infinite set of images as possible solutions. Traditionally, this is tackled as a reconstruction problem by…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
Linearity is an important and frequently sought property in electronics and instrumentation. Here, we report a method capable of, given a transfer function, identifying the respective most linear region of operation with a fixed width. This…
We study time-harmonic Maxwell's equations in meta-materials that use either perfect conductors or high-contrast materials. Based on known effective equations for perfectly conducting inclusions, we calculate the transmission and reflection…
We will present a new method, which enables us to find threshold functions for many properties in random intersection graphs. This method will be used to establish sharp threshold functions in random intersection graphs for k-connectivity,…
EASAL (Efficient Atlasing and Sampling of Assembly Landscapes) is a geometric method for sampling and computing integrals over the potential energy landscape of small molecular assemblies. EASAL's efficiency arises from the fact that small…
We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…
Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…
We consider an alternative way of obtaining the effective elastic properties of a cracked medium. Similarly, to the popular linear-slip model, we assume flat, parallel fractures, and long wavelengths. However, we do not treat fractures as…