410 citations · 713 across the 33 of their papers we have counts for
39 papers
A provably convergent MM-GKS variant for large-scale inverse problems
Mirjeta Pasha, Eric de Sturler, Misha Kilmer
For high-quality images with sharp edges, a popular choice for edge-preserving regularization is using a general(ized) -norm of the gradient of the image. This can be imple…
A Symmetry-Preserving Tensor -SVD
Victor Arsenescu, Misha E. Kilmer
Multiway data such as image collections and video is ubiquitous, but the usual approach of flattening them into matrices discards the cross-mode structure that often carries the si…
Wavelet-based multilevel framework for -regularized image deblurring
Danyh Tolah, Malena I. Español, Misha E. Kilmer
Solving large-scale -regularized image deblurring problems efficiently while preserving sharp edges remains a significant computational challenge. We propose a wavelet-base…
Structure-Informed Bounds on the Kronecker Rank of Block-Structured Matrices
Allison Fuller, Malena Español, Misha Kilmer
We derive theoretical bounds on the Kronecker rank of block-structured matrices that possess both inner and outer structure. Building on the matrix-to-tensor and tensor-to-matrix f…
Nonlinear RMM-GKS for Large-Scale Dynamic and Streaming Inverse Problems with Uncertain Forward Operators
Toluwani Okunola, Mirjeta Pasha, Misha E. Kilmer +2
Many practical imaging systems suffer from uncertainty in acquisition geometry -- such as projection angles in computed tomography or sensor positions in photoacoustic tomography -…
Exact Symmetry as Algebra: Group-Structured Tensors that Enforce Physical Selection Rules
Paulina Hoyos, Shashanka Ubaru, Dongsung Huh +5
Symmetry determines which physical responses of molecules and crystals are allowed and underlies many models used throughout the physical sciences. Yet several widely used machine-…
An Efficient Cumulative Edge-Detection Method for Image Reconstruction
Toluwani Okunola, Mirjeta Pasha, Misha E. Kilmer
When reconstructing images from noisy measurements, such as in medical scans or scientific imaging, we face an inverse problem: recovering an unknown image from indirect, corrupted…
A tensor-based dynamic mode decomposition based on the -product
Arvind K. Saibaba, Misha E. Kilmer, Khalil Hall-Hooper +2
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applicat…
Alternating steepest descent methods for tensor completion with applications to spectromicroscopy
Oliver Townsend, Sergey Dolgov, Silvia Gazzola +1
In this paper we develop two new Tensor Alternating Steepest Descent algorithms for tensor completion in the low-rank -product format, whereby we aim to reconstruct an e…
Efficient Dynamic Image Reconstruction with motion estimation
Toluwani Okunola, Mirjeta Pasha, Misha Kilmer +1
Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale natu…
Tensor Completion with BMD Factor Nuclear Norm Minimization
Fan Tian, Mirjeta Pasha, Misha E. Kilmer +2
This paper is concerned with the problem of recovering third-order tensor data from limited samples. A recently proposed tensor decomposition (BMD) method has been shown to efficie…
Recycling MMGKS for large-scale dynamic and streaming data
Mirjeta Pasha, Eric de Sturler, Misha E. Kilmer
Reconstructing high-quality images with sharp edges requires the use of edge-preserving constraints in the regularized form of the inverse problem. The use of the -norm on…
Multigrid preconditioning for regularized least-squares problems
Matthias Bolten, Scott P. MacLachlan, Misha E. Kilmer
In this paper, we are concerned with efficiently solving the sequences of regularized linear least squares problems associated with employing Tikhonov-type regularization with regu…
Subspace Recycling for Sequences of Shifted Systems with Applications in Image Recovery
Misha E. Kilmer, Eric de Sturler
For many applications involving a sequence of linear systems with slowly changing system matrices, subspace recycling, which exploits relationships among systems and reuses search…
Tensor BM-Decomposition for Compression and Analysis of Video Data
Fan Tian, Misha E. Kilmer, Eric Miller +1
Given tensors of size , , and , respect…
Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)
Ege Ozsar, Misha Kilmer, Eric Miller +2
We introduce PaLEnTIR, a significantly enhanced parametric level-set (PaLS) method addressing the restoration and reconstruction of piecewise constant objects. Our key contribution…
Efficient randomized tensor-based algorithms for function approximation and low-rank kernel interactions
Arvind K. Saibaba, Rachel Minster, Misha E. Kilmer
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tuck…
Structured Matrix Approximations via Tensor Decompositions
Misha E. Kilmer, Arvind K. Saibaba
We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g.,…
A survey of subspace recycling iterative methods
Kirk M. Soodhalter, Eric de Sturler, Misha Kilmer
This survey concerns subspace recycling methods, a popular class of iterative methods that enable effective reuse of subspace information in order to speed up convergence and find…
Tensor-Tensor Products for Optimal Representation and Compression
Misha Kilmer, Lior Horesh, Haim Avron +1
In this era of big data, data analytics and machine learning, it is imperative to find ways to compress large data sets such that intrinsic features necessary for subsequent analys…
An Inner-Outer Iterative Method for Edge Preservation in Image Restoration and Reconstruction
Silvia Gazzola, Misha E. Kilmer, James G. Nagy +2
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalizati…
Dynamic Graph Convolutional Networks Using the Tensor M-Product
Osman Asif Malik, Shashanka Ubaru, Lior Horesh +2
Many irregular domains such as social networks, financial transactions, neuron connections, and natural language constructs are represented using graph structures. In recent years,…
Non-negative Tensor Patch Dictionary Approaches for Image Compression and Deblurring Applications
Elizabeth Newman, Misha E. Kilmer
In recent work (Soltani, Kilmer, Hansen, BIT 2016), an algorithm for non-negative tensor patch dictionary learning in the context of X-ray CT imaging and based on a tensor-tensor p…
Randomized algorithms for low-rank tensor decompositions in the Tucker format
Rachel Minster, Arvind K. Saibaba, Misha E. Kilmer
Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored i…