Related papers: Semi-Sparsity for Smoothing Filters

Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…

This letter proposes a novel sparsity-aware adaptive filtering scheme and algorithms based on an alternating optimization strategy with shrinkage. The proposed scheme employs a two-stage structure that consists of an alternating…

Single-molecule localization microscopy techniques, like stochastic optical reconstruction microscopy (STORM), visualize biological specimens by stochastically exciting sparse blinking emitters. The raw images suffer from unwanted…

Classical convergence analyses for optimization algorithms rely on the widely-adopted uniform smoothness assumption. However, recent experimental studies have demonstrated that many machine learning problems exhibit non-uniform smoothness,…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

We propose a new first-order optimisation algorithm to solve high-dimensional non-smooth composite minimisation problems. Typical examples of such problems have an objective that decomposes into a non-smooth empirical risk part and a…

While deep neural networks (DNNs) have proven to be efficient for numerous tasks, they come at a high memory and computation cost, thus making them impractical on resource-limited devices. However, these networks are known to contain a…

Image smoothing is a fundamental procedure in applications of both computer vision and graphics. The required smoothing properties can be different or even contradictive among different tasks. Nevertheless, the inherent smoothing nature of…

Traditional unsupervised optical flow methods are vulnerable to occlusions and motion boundaries due to lack of object-level information. Therefore, we propose UnSAMFlow, an unsupervised flow network that also leverages object information…

We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and…

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can benefit…

A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…

A polynomial matrix inequality is a formula asserting that a polynomial matrix is positive semidefinite. Polynomial matrix optimization concerns minimizing the smallest eigenvalue of a symmetric polynomial matrix subject to a tuple of…

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is…

We consider the unconstrained optimization problem whose objective function is composed of a smooth and a non-smooth conponents where the smooth component is the expectation a random function. This type of problem arises in some interesting…

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…

Sparse decomposition has been widely used for different applications, such as source separation, image classification, image denoising and more. This paper presents a new algorithm for segmentation of an image into background and foreground…

Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes…

Sparse connectivity is a hallmark of the brain and a desired property of artificial neural networks. It promotes energy efficiency, simplifies training, and enhances the robustness of network function. Thus, a detailed understanding of how…

In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…