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UID:166@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20260105T150000
DTEND;TZID=Asia/Kolkata:20260105T160000
DTSTAMP:20251205T092804Z
URL:https://cds.iisc.ac.in/events/ph-d-thesis-colloquium-102-cds-05-januar
 y-2026-tensor-generalized-inverses-and-low-rank-representation-with-applic
 ations/
SUMMARY:Ph.D: Thesis Colloquium: 102 : CDS: 05\, January 2026 "Tensor gener
 alized inverses and low-rank representation with applications"
DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\nPh.D. Thesis Col
 loquium\n\n\n\nSpeaker: Mr. Biswarup Karmakar\nS.R. Number: 06-18-01-10-12
 -22-1-21055\nTitle: Tensor generalized inverses and low-rank representatio
 n with applications\nResearch Supervisor: Dr. Ratikanta Behera\nDate &amp\
 ; Time : January 05 2026 (Monday)\, 15:00 PM\nVenue : #102\, CDS Seminar H
 all\n\n\n\nABSTRACT\nTensors are mathematical structures that generalize v
 ectors and matrices to higher dimensions\, providing efficient computation
 al frameworks for multidimensional data while preserving inter-channel rel
 ationships that conventional methods cannot capture. Advanced tensor opera
 tion techniques\, such as the t-product and M-product\, enable Fourier dom
 ain computations and mode-product operations\, respectively\, for flexible
  factorizations. These establish rigorous foundations for decomposition al
 gorithms\, data recovery\, and dimensionality reduction while maintaining 
 a multilinear structure. Tensor-based paradigms have advantages in scalabl
 e machine learning and the recovery of incomplete data problems.\n\nThis d
 issertation establishes comprehensive analytical and algorithmic framework
 s within the t-product and M-product theoretical paradigms for tensor gene
 ralized inverses and low-rank recovery methodologies\, with applications i
 n high-dimensional signal and image processing. The first contribution int
 roduces a novel M-QDR decomposition under the M-product framework for comp
 uting tensor generalized inverses without involving square-root terms\, th
 ereby preserving the algebraic structure and enabling the exact computatio
 n of the Moore-Penrose and outer inverses of tensors. The second contribut
 ion presents efficient iterative algorithms for computing the tensor Moore
 -Penrose inverse within the t-product framework\, utilizing FFT-based diag
 onalization to decompose tensor operations into independent matrix computa
 tions\, thereby enhancing tensor least-squares and image restoration appli
 cations. The third contribution establishes a robust tensor completion fra
 mework employing weighted correlated total variation norms under the M-pro
 duct\, incorporating weighted Schatten-p norms on gradient tensors for low
 -rank regularization and weighted $l_1$ norms for noise suppression\, impl
 emented through an enhanced alternating direction method of multipliers so
 lver for reliable reconstruction in image completion and denoising. Furthe
 r\, iterative methods for quaternion tensor generalized inverses are devel
 oped to process multichannel data as unified entities\, preserving inter-c
 hannel relationships for applications in 3D signal processing\, color imag
 e inpainting\, and video deblurring. This study establishes a unified fami
 ly of tensor and quaternion computational methods that significantly advan
 ce high-dimensional data reconstruction methodologies. Finally\, a tensor 
 deep unfolding framework is proposed for hyperspectral and multispectral i
 mage reconstruction\, which transforms iterative optimization steps into l
 earnable neural modules that integrate interpretability with data-driven a
 daptability. In conclusion\, this dissertation lays the groundwork for fut
 ure studies on tensors that explore the solution of PDEs\, parallel implem
 entations\, and hypergraph applications.\n\n\n\nALL ARE WELCOME
CATEGORIES:Events,Ph.D. Thesis Colloquium
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