We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the non-convex case and derive worst case complexities that are equal or better than existing methods. We show applications to total variation based 2D image pro...

In this paper we present a novel 3-D free-form non-rigid registration algorithm which combines the mutual information similarity measure with a particular curvature based regularizer, which has been demonstrated to produce very satisfactory results in conjunction with the sum of squared differences distance measure. The method is evaluated for inter-subject MR brain image registration using sim...

We view regularized learning of a function in a Banach space from its finite samples as an optimization problem. Within the framework of reproducing kernel Banach spaces, we prove the representer theorem for the minimizer of regularized learning schemes with a general loss function and a nondecreasing regularizer. When the loss function and the regularizer are differentiable, a characterization...

Purpose: The goal of this study is to develop a novel deep learning (DL) based reconstruction framework improve the digital breast tomosynthesis (DBT) imaging performance. Methods: In work, DIR-DBTnet developed for DBT image by unrolling standard iterative algorithm within framework. particular, such network learns regularizer and iteration parameters automatically through training with large a...

<span>Variational active contour seeks to segment or extract desired object boundaries for further analysis. The model can be divided into global segmentation and selective segmentation. Selective segmentation, which focuses on segmenting a particular object, is preferable the model. Recently, number of models have been developed precisely an grayscale images. Nevertheless, if input image...

The celebrated Nesterov’s accelerated gradient method offers great speed-ups compared to the classical gradient descend method as it attains the optimal first-order oracle complexity for smooth convex optimization. On the other hand, the popular AdaGrad algorithm competes with mirror descent under the best regularizer by adaptively scaling the gradient. Recently, it has been shown that the acce...

As recently discussed by Bar, Kiryati, and Sochen in [3], the Ambrosio-Tortorelli approximation of the Mumford-Shah functional defines an extended line process regularization where the regularizer has an additional constraint introduced by the term ρ|∇v|. This term mildly forces some spatial organization by demanding that the edges are smooth. However, it does not force spatial coherence such a...

Abstract Existing deep unfolding methods unroll an optimization algorithm with a fixed number of steps, and utilize convolutional neural networks (CNNs) to learn data-driven priors. However, their performance is limited for two main reasons. Firstly, priors learned in feature space need be converted the image at each iteration step, which limits depth CNNs prevents from exploiting contextual in...