Related papers: Convolutional Dictionary Learning: Acceleration an…

This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…

Convolutional operator learning is gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called patch-domain approaches that extract and store many overlapping patches across…

Convolutional Dictionary Learning (CDL) has emerged as a powerful approach for signal representation by learning translation-invariant features through convolution operations. While existing CDL methods are predominantly designed and used…

Most existing convolutional dictionary learning (CDL) algorithms are based on batch learning, where the dictionary filters and the convolutional sparse representations are optimized in an alternating manner using a training dataset. When…

Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to multidimensional data. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. As estimated…

This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…

We propose a novel structured discriminative block-diagonal dictionary learning method, referred to as scalable Locality-Constrained Projective Dictionary Learning (LC-PDL), for efficient representation and classification. To improve the…

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a…

The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…

Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers…

The alternating direction method with multipliers (ADMM) has been one of most powerful and successful methods for solving various convex or nonconvex composite problems that arise in the fields of image & signal processing and machine…

Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of…

Convolutional sparse representation (CSR), shift-invariant model for inverse problems, has gained much attention in the fields of signal/image processing, machine learning and computer vision. The most challenging problems in CSR implies…

As a well-known optimization framework, the Alternating Direction Method of Multipliers (ADMM) has achieved tremendous success in many classification and regression applications. Recently, it has attracted the attention of deep learning…

The Convolutional Sparse Coding (CSC) model has recently gained considerable traction in the signal and image processing communities. By providing a global, yet tractable, model that operates on the whole image, the CSC was shown to…

The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective…

Diffusion Language Models (DLMs) offer a promising parallel generation paradigm but suffer from slow inference due to numerous refinement steps and the inability to use standard KV caching. We introduce CDLM (Consistency Diffusion Language…

We propose a novel Bregman descent algorithm for minimizing a convex function that is expressed as the sum of a differentiable part (defined over an open set) and a possibly nonsmooth term. The approach, referred to as the Variable Bregman…

Stochastic gradient descent (SGD) and its many variants are the widespread optimization algorithms for training deep neural networks. However, SGD suffers from inevitable drawbacks, including vanishing gradients, lack of theoretical…