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This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is…
Regularized optimization has been a classical approach to solving imaging inverse problems, where the regularization term enforces desirable properties of the unknown image. Recently, the integration of flow matching generative models into…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
The classification of medical images is a pivotal aspect of disease diagnosis, often enhanced by deep learning techniques. However, traditional approaches typically focus on unimodal medical image data, neglecting the integration of diverse…
Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…
This study develops a graph search algorithm to find the optimal discrimination path for the binary classification problem. The objective function is defined as the difference of variations between the true positive (TP) and false positive…
Standard contrastive learning approaches usually require a large number of negatives for effective unsupervised learning and often exhibit slow convergence. We suspect this behavior is due to the suboptimal selection of negatives used for…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping…
This thesis develops a general theoretical and numerical framework for achieving high-contrast atom interferometry based on double Bragg diffraction (DBD). While DBD offers intrinsic symmetry, reduced sensitivity to internal-state…
The existing contrastive learning methods mainly focus on single-grained representation learning, e.g., part-level, object-level or scene-level ones, thus inevitably neglecting the transferability of representations on other granularity…
Parkinson's disease (PD) is a progressive neurodegenerative condition characterized by the death of dopaminergic neurons, leading to various movement disorder symptoms. Early diagnosis of PD is crucial to prevent adverse effects, yet…
FPGAs provide a flexible and efficient platform to accelerate rapidly-changing algorithms for computer vision. The majority of existing work focuses on accelerating image classification, while other fundamental vision problems, including…
We propose a new modified primal-dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates…
Selecting the fastest algorithm for a specific signal/image processing task is a challenging question. We propose an approach based on the Performance Estimation Problem framework that numerically and automatically computes the worst-case…
Image subtraction in astronomy is a tool for transient object discovery such as asteroids, extra-solar planets and supernovae. To match point spread functions (PSFs) between images of the same field taken at different times a convolution…
In multi-contrast magnetic resonance imaging (MRI), compressed sensing theory can accelerate imaging by sampling fewer measurements within each contrast. The conventional optimization-based models suffer several limitations: strict…
Many techniques for real-time trajectory optimization and control require the solution of optimization problems at high frequencies. However, ill-conditioning in the optimization problem can significantly reduce the speed of first-order…
In this paper, we implemented both sequential and parallel version of fractal image compression algorithms using CUDA (Compute Unified Device Architecture) programming model for parallelizing the program in Graphics Processing Unit for…