相关论文: Constructing test instances for Basis Pursuit Deno…

This thesis presents two similarity-based approaches to sparse data problems. The first approach is to build soft, hierarchical clusters: soft, because each event belongs to each cluster with some probability; hierarchical, because cluster…

The sparsity constrained rank-one matrix approximation problem is a difficult mathematical optimization problem which arises in a wide array of useful applications in engineering, machine learning and statistics, and the design of…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…

Learning-based denoising algorithms achieve state-of-the-art performance across various denoising tasks. However, training such models relies on access to large training datasets consisting of clean and noisy image pairs. On the other hand,…

This work treats the recovery of sparse, binary signals through box-constrained basis pursuit using biased measurement matrices. Using a probabilistic model, we provide conditions under which the recovery of both sparse and saturated binary…

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this…

Supervised training for real-world denoising presents challenges due to the difficulty of collecting large datasets of paired noisy and clean images. Recent methods have attempted to address this by utilizing unpaired datasets of clean and…

The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse…

We study the problem of recovering the latent ground truth labeling of a structured instance with categorical random variables in the presence of noisy observations. We present a new approximate algorithm for graphs with categorical…

Parsimonious representations are ubiquitous in modeling and processing information. Motivated by the recent Multi-Layer Convolutional Sparse Coding (ML-CSC) model, we herein generalize the traditional Basis Pursuit problem to a multi-layer…

We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson…

Regularization by the sum of singular values, also referred to as the trace norm, is a popular technique for estimating low rank rectangular matrices. In this paper, we extend some of the consistency results of the Lasso to provide…

This paper adapts a popular image quality measure called structural similarity for high precision registration based tracking while also introducing a simpler and faster variant of the same. Further, these are evaluated comprehensively…

Enhancing the visibility in extreme low-light environments is a challenging task. Under nearly lightless condition, existing image denoising methods could easily break down due to significantly low SNR. In this paper, we systematically…

This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…

Imitation learning has emerged as a promising approach for addressing sequential decision-making problems, with the assumption that expert demonstrations are optimal. However, in real-world scenarios, most demonstrations are often…

We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…

The success of diffusion models has driven interest in performing conditional sampling via training-free guidance of the denoising process to solve image restoration and other inverse problems. A popular class of methods, based on Diffusion…