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Panoramic Video Separation with Online Grassmannian Robust Subspace Estimation

Published in 2019 Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) - Workshop, 2019

In this work, we propose a new total variation (TV)-regularized robust principal component analysis (RPCA) algorithm for panoramic video data with incremental gradient descent on the Grassmannian.

Recommended citation: Kyle Gilman and Laura Balzano. (2019). "Panoramic Video Separation with Online Grassmannian Robust Subspace Estimation." Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) . https://ieeexplore.ieee.org/document/9022344

Online Tensor Completion and Free Submodule Tracking with the t-SVD

Published in 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020

We propose a new online algorithm, called TOUCAN, for the tensor completion problem of imputing missing entries of a low tubal-rank tensor using the tensor-tensor product (t- product) and tensor singular value decomposition (t-SVD) algebraic framework.

Recommended citation: Kyle Gilman and Laura Balzano. (2020). "Online Tensor Completion and Free Submodule Tracking with the t-SVD." 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). https://ieeexplore.ieee.org/document/9053199

HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise

Published in IEEE Transactions on Signal Processing, Vol. 69, 2021

This paper develops a probabilistic PCA variant that estimates and accounts for this heterogeneity by incorporating it in the statistical model.

Recommended citation: David Hong, Kyle Gilman, Laura Balzano, and Jeffrey A. Fessler. "HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise " IEEE Transactions on Signal Processing, Vol. 69, 2021 https://ieeexplore.ieee.org/document/9514397

Grassmannian Optimization for Online Tensor Completion and Tracking with the t-SVD

Published in IEEE Transactions on Signal Processing, Vol. 70, 2022, 2022

We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework.

Recommended citation: Kyle Gilman, Davoud Ataee Tarzanagh, and Laura Balzano (2022). "Grassmannian Optimization for Online Tensor Completion and Tracking with the t-SVD." IEEE Transactions on Signal Processing, Vol. 70, 2022. https://ieeexplore.ieee.org/abstract/document/9756209)

A Semidefinite Relaxation for Sums of Heterogeneous Quadratics on the Stiefel Manifold

Published in arXiv, 2022

We study the maximization of sums of heterogeneous quadratic functions over the Stiefel manifold, a nonconvex problem that arises in several modern signal processing and machine learning applications such as heteroscedastic probabilistic principal component analysis (HPPCA).

Recommended citation: Kyle Gilman, Sam Burer, and Laura Balzano (2022). "A Semidefinite Relaxation for Sums of Heterogeneous Quadratics on the Stiefel Manifold." arXiv preprint arXiv:2205.13653. https://arxiv.org/abs/2205.13653