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Ground-state energy and matrix element are reconstructed from correlators in lattice QCD by diagonalizing transfer matrix $\hat{T}$ within the Krylov subspace spanned by $\hat{T}^n|\chi\rangle$, where $|\chi\rangle$ is a state generated by…
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is…
Accelerating the data acquisition of dynamic magnetic resonance imaging (MRI) leads to a challenging ill-posed inverse problem, which has received great interest from both the signal processing and machine learning community over the last…
With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted…
We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an antisymmetric constant matrix. Via this reduction, we obtain a…
While MCMC methods have become a main work-horse for Bayesian inference, scaling them to large distributed datasets is still a challenge. Embarrassingly parallel MCMC strategies take a divide-and-conquer stance to achieve this by writing…
Bilevel optimization, with broad applications in machine learning, has an intricate hierarchical structure. Gradient-based methods have emerged as a common approach to large-scale bilevel problems. However, the computation of the…
This report investigates the extension of the Bayesian Subspace System Identification method proposed in our previous work to the Multiple-Input Multiple-Output (MIMO) case. We derive new equivariant priors and posterior distributions…
We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…
The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the…
One of the limitations of recycled GCRO methods is the large amount of computation required to orthogonalize the basis vectors of the newly generated Krylov subspace for the approximate solution when combined with those of the recycle…
In today's digital world, which has many different types of media, steganography, the art of secret communication, has a lot of problems to deal with. Traditional methods are often fixed and only work with one type of carrier media. This…
Selection among alternative theoretical models given an observed data set is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing…
Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…
Krylov subspace, which is generated by multiplying a given vector by the matrix of a linear transformation and its successive powers, has been extensively studied in classical optimization literature to design algorithms that converge…
Recent studies show that deep learning (DL) based MRI reconstruction outperforms conventional methods, such as parallel imaging and compressed sensing (CS), in multiple applications. Unlike CS that is typically implemented with…
This presentation abstract, presented at 12th Applied Inverse Problems Conference, to be held at FGV EMAp, Rio de Janeiro, Brazil, in 2025, describe the theory results of applying the Chebyshev pseudospectral method (CPM) to reconstruct the…
We introduce a new formulation of the Hidden Parameter Markov Decision Process (HiP-MDP), a framework for modeling families of related tasks using low-dimensional latent embeddings. Our new framework correctly models the joint uncertainty…
In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…
Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the…