Related papers: Efficient Decomposition-Based Algorithms for $\ell…
Sparsity regularization has garnered significant interest across multiple disciplines, including statistics, imaging, and signal processing. Standard techniques for addressing sparsity regularization include iterative soft thresholding…
Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…
We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…
It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal…
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…
We introduce a linear operator on a Hilbert $C^*$-module for analyzing skew-product dynamical systems. The operator is defined by composition and multiplication. We show that it admits a decomposition in the Hilbert $C^*$-module, called…
Embedded computer vision applications increasingly require the speed and power benefits of single-precision (32 bit) floating point. However, applications which make use of Levenberg-like optimization can lose significant accuracy when…
Extending the idea of Even and Lehrer [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of…
SVD (singular value decomposition) is one of the basic tools of machine learning, allowing to optimize basis for a given matrix. However, sometimes we have a set of matrices $\{A_k\}_k$ instead, and would like to optimize a single common…
This paper proposes a joint decomposition method that combines La- grangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global…
The conventional way of formulating inverse problems such as identification of a (possibly infinite dimensional) parameter, is via some forward operator, which is the concatenation of the observation operator with the parameter-to-state-map…
For arbitrarily small values of $\varepsilon>0,$ we formulate and analyse the Maxwell system of equations of electromagnetism on $\varepsilon$-periodic sets $S^\varepsilon\subset{\mathbb R}^3.$ Assuming that a family of Borel measures…
We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm…
We consider a class of regularization methods for inverse problems where a coupled regularization is employed for the simultaneous reconstruction of data from multiple sources. Applications for such a setting can be found in multi-spectral…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
The joint approximate diagonalization of non-commuting symmetric matrices is an important process in independent component analysis. This problem can be formulated as an optimization problem on the Stiefel manifold that can be solved using…
Image deblurring is a fundamental problem in imaging, usually solved with com-putationally intensive optimization procedures. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur…
Convolution and transposed convolution are fundamental operators widely used in neural networks. However, transposed convolution (a.k.a. deconvolution) does not serve as a true inverse of convolution due to inherent differences in their…
We present two algorithms for constructing orthonormal bases of rational function vectors with respect to a discrete inner product, and discuss how to use them for a rational approximation problem. Building on the pencil-based formulation…
Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special…