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Time-varying graph signal recovery has been widely used in many applications, including climate change, environmental hazard monitoring, and epidemic studies. It is crucial to choose appropriate regularizations to describe the…

Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in machine learning. Reasons for this include its simplicity, speed and stability, as well as its competitive performance on $\ell_1$…

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…

We contribute to the growing body of knowledge on more powerful and adaptive stepsizes for convex optimization, empowered by local curvature information. We do not go the route of fully-fledged second-order methods which require the…

The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In this paper, in order to alleviate the staircase effect,…

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its…

Randomized coordinate descent (RCD) methods are state-of-the-art algorithms for training linear predictors via minimizing regularized empirical risk. When the number of examples ($n$) is much larger than the number of features ($d$), a…

Computer vision methods typically optimize for first-order dynamics (e.g., optical flow). However, in many cases the properties of interest are subtle variations in higher-order changes, such as acceleration. This is true in the cardiac…

This paper introduces a novel method for the efficient second-order accurate computation of normal fields from volume fractions on unstructured polyhedral meshes. Locally, i.e. in each mesh cell, an averaged normal is reconstructed by…

Deep convolutional neural networks (CNNs) are broadly considered to be state-of-the-art generic end-to-end image classification systems. However, they are known to underperform when training data are limited and thus require data…

Bilinear pooling of Convolutional Neural Network (CNN) features [22, 23], and their compact variants [10], have been shown to be effective at fine-grained recognition, scene categorization, texture recognition, and visual question-answering…

Deep convolutional neural networks perform better on images containing spatially invariant degradations, also known as synthetic degradations; however, their performance is limited on real-degraded photographs and requires multiple-stage…

Manifold-valued signal- and image processing has received attention due to modern image acquisition techniques. Recently, a convex relaxation of the otherwise nonconvex Tikhonov-regularization for denoising circle-valued data has been…

Nonlocal patch-based methods, in particular the Bayes' approach of Lebrun, Buades and Morel (2013), are considered as state-of-the-art methods for denoising (color) images corrupted by white Gaussian noise of moderate variance. This paper…

The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…

We propose an unsupervised approach for learning end-to-end reconstruction operators for ill-posed inverse problems. The proposed method combines the classical variational framework with iterative unrolling, which essentially seeks to…

Storage systems often rely on multiple copies of the same compressed data, enabling recovery in case of binary data errors, of course, at the expense of a higher storage cost. In this paper we show that a wiser method of duplication entails…

In the context of image processing, given a $k$-th order, homogeneous and linear differential operator with constant coefficients, we study a class of variational problems whose regularizing terms depend on the operator. Precisely, the…

Ultrasound is the second most used modality in medical imaging. It is cost effective, hazardless, portable and implemented routinely in numerous clinical procedures. Nonetheless, image quality is characterized by granulated appearance, poor…

The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…