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A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
Signal decomposition (SD) approaches aim to decompose non-stationary signals into their constituent amplitude- and frequency-modulated components. This represents an important preprocessing step in many practical signal processing…
Image segmentation has come a long way since the early days of computer vision, and still remains a challenging task. Modern variations of the classical (purely bottom-up) approach, involve, e.g., some form of user assistance (interactive…
We study and develop (stochastic) primal--dual block-coordinate descent methods for convex problems based on the method due to Chambolle and Pock. Our methods have known convergence rates for the iterates and the ergodic gap: $O(1/N^2)$ if…
This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
This paper addresses fundamental scaling issues that hinder phase retrieval (PR) in high dimensions. We show that, if the measurement matrix can be put into a generalized block-diagonal form, a large PR problem can be solved on separate…
The approximate joint diagonalization of a set of matrices consists in finding a basis in which these matrices are as diagonal as possible. This problem naturally appears in several statistical learning tasks such as blind signal…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly…
High-dimensional image data often require dimensionality reduction before further analysis. This paper provides a purely analytical comparison of two linear techniques-Principal Component Analysis (PCA) and Singular Value Decomposition…
Objective: Model based deep learning (MBDL) has been challenging to apply to the reconstruction of 3D non-Cartesian MRI acquisitions due to extreme GPU memory demand (>250 GB using traditional backpropagation) primarily because the entire…
The approximate joint diagonalization (AJD) is an important analytic tool at the base of numerous independent component analysis (ICA) and other blind source separation (BSS) methods, thus finding more and more applications in medical…
The singular value decomposition (SVD) and the principal component analysis are fundamental tools and probably the most popular methods for data dimension reduction. The rapid growth in the size of data matrices has lead to a need for…
The increased quantity of data has led to a soaring use of networks to model relationships between different objects, represented as nodes. Since the number of nodes can be particularly large, the network information must be summarised…
Inducing-point-based sparse variational Gaussian processes have become the standard workhorse for scaling up GP models. Recent advances show that these methods can be improved by introducing a diagonal scaling matrix to the conditional…
This article considers the recovery of low-rank matrices via a convex nuclear-norm minimization problem and presents two null space properties (NSP) which characterize uniform recovery for the case of block-diagonal matrices and…
Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…
In this paper, we introduce innovative approaches for accelerating the Jacobi method for matrix diagonalization, specifically through the formulation of large matrix diagonalization as a Semi-Markov Decision Process and small matrix…
The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…