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Structured illumination microscopy (SIM) has become an important technique for optical super-resolution imaging because it allows a doubling of image resolution at speeds compatible for live-cell imaging. However, the reconstruction of SIM…
We consider the problem of finding the spectrum of an operator taking the form of a low-rank (rank one or two) non-normal perturbation of a well-understood operator, motivated by a number of problems of applied interest which take this…
Hidden Markov models (HMMs) are widely used statistical models for modeling sequential data. The parameter estimation for HMMs from time series data is an important learning problem. The predominant methods for parameter estimation are…
We introduce SAM4MLLM, an innovative approach which integrates the Segment Anything Model (SAM) with Multi-Modal Large Language Models (MLLMs) for pixel-aware tasks. Our method enables MLLMs to learn pixel-level location information without…
In this thesis, the numerical solution of three different classes of problems have been studied. Specifically, new techniques have been proposed and their theoretical analysis has been performed, accompanied by a wide set of numerical…
We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a…
Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization…
Large language models and deep neural networks achieve strong performance but suffer from reliability issues and high computational cost. This thesis proposes a unified framework based on spectral geometry and random matrix theory to…
Hyperspectral sensors capture dense spectra per pixel but suffer from low spatial resolution, causing blurred boundaries and mixed-pixel effects. Co-registered companion sensors such as multispectral, RGB, or panchromatic cameras provide…
The traditional Transformer model encounters challenges with variable-length input sequences, particularly in Hyperspectral Image Classification (HSIC), leading to efficiency and scalability concerns. To overcome this, we propose a…
Computer based recognition and detection of abnormalities in ECG signals is proposed. For this purpose, the Support Vector Machines (SVM) are combined with the advantages of Hermite transform representation. SVM represent a special type of…
This paper has proposed the GMRES that augments Krylov subspaces with a set of approximate right singular vectors. The proposed method suppresses the error norms of a linear system of equations. Numerical experiments comparing the proposed…
Spectral variability is one of the major issue when conducting hyperspectral unmixing. Within a given image composed of some elementary materials (herein referred to as endmember classes), the spectral signature characterizing these classes…
We provide a comparative study of the Subspace Projected Approximate Matrix method, abbreviated SPAM, which is a fairly recent iterative method to compute a few eigenvalues of a Hermitian matrix $A$. It falls in the category of inner-outer…
Implicit representation mapping (IRM) can translate image features to any continuous resolution, showcasing its potent capability for ultra-high-resolution image segmentation refinement. Current IRM-based methods for refining…
In this work, we combine Beyn's method and the recently developed recursive integral method (RIM) to propose a contour integral-based, region partitioning eigensolver for nonlinear eigenvalue problems. A new partitioning criterion is…
Hyperspectral image (HSI) classification is a hot topic in the remote sensing community. This paper proposes a new framework of spectral-spatial feature extraction for HSI classification, in which for the first time the concept of deep…
Memristive Processing In-Memory (PIM) is one of the promising techniques for overcoming the Von-Neumann bottleneck. Reduction of data transfer between processor and memory and data processing by memristors in data-intensive applications…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue…