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In the realm of signal and image denoising and reconstruction, $\ell_1$ regularization techniques have generated a great deal of attention with a multitude of variants. A key component for their success is that under certain assumptions,…

Numerical Analysis · Mathematics 2018-03-30 Toby Sanders , Rodrigo B. Platte

This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary…

Image and Video Processing · Electrical Eng. & Systems 2024-04-29 Elena Morotti , Davide Evangelista , Andrea Sebastiani , Elena Loli Piccolomini

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor…

Computer Vision and Pattern Recognition · Computer Science 2014-12-11 Giovanni Chierchia , Nelly Pustelnik , Beatrice Pesquet-Popescu , Jean-Christophe Pesquet

Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…

Optimization and Control · Mathematics 2020-10-20 Hamza Cherkaoui , Jeremias Sulam , Thomas Moreau

Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…

Computer Vision and Pattern Recognition · Computer Science 2019-07-24 Marcus Valtonen Örnhag , Carl Olsson , Anders Heyden

Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…

Methodology · Statistics 2020-08-17 Ana F. Vidal , Valentin De Bortoli , Marcelo Pereyra , Alain Durmus

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…

Numerical Analysis · Mathematics 2017-10-13 Ernesto De Vito , Massimo Fornasier , Valeriya Naumova

Popular methods for finding regularized solutions to inverse problems include sparsity promoting $\ell_1$ regularization techniques, one in particular which is the well known total variation (TV) regularization. More recently, several…

Numerical Analysis · Mathematics 2017-03-22 Toby Sanders

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…

Optimization and Control · Mathematics 2024-11-05 Pengyu Chen , Xu Shi , Rujun Jiang , Jiulin Wang

We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…

Robotics · Computer Science 2023-09-19 Mohamad Qadri , Zachary Manchester , Michael Kaess

Total Variation (TV) based regularization has been widely applied in restoration problems due to its simple derivative filters based formulation and robust performance. While first order TV suffers from staircase effect, second order TV…

Signal Processing · Electrical Eng. & Systems 2019-04-08 Sanjay Viswanath , Muthuvel Arigovindan

Neural networks have become ubiquitous tools for solving signal and image processing problems, and they often outperform standard approaches. Nevertheless, training neural networks is a challenging task in many applications. The prevalent…

Optimization and Control · Mathematics 2022-10-28 Patrick L. Combettes , Jean-Christophe Pesquet , Audrey Repetti

Bilevel optimization, crucial for hyperparameter tuning, meta-learning and reinforcement learning, remains less explored in the decentralized learning paradigm, such as decentralized federated learning (DFL). Typically, decentralized…

Machine Learning · Computer Science 2024-10-21 Min Wen , Chengchang Liu , Ahmed Abdelmoniem , Yipeng Zhou , Yuedong Xu

Tensor completion and tensor decomposition are important problems in many domains. In this work, we leverage the connection between these problems to learn a distance metric that improves both decomposition and completion. We show that the…

Optimization and Control · Mathematics 2022-09-02 Maryam Bagherian , Davoud A. Tarzanagh , Ivo Dinov , Joshua D. Welch

The crux of self-supervised video representation learning is to build general features from unlabeled videos. However, most recent works have mainly focused on high-level semantics and neglected lower-level representations and their…

Computer Vision and Pattern Recognition · Computer Science 2021-08-18 Rui Qian , Yuxi Li , Huabin Liu , John See , Shuangrui Ding , Xian Liu , Dian Li , Weiyao Lin

Due to the hierarchical structure of many machine learning problems, bilevel programming is becoming more and more important recently, however, the complicated correlation between the inner and outer problem makes it extremely challenging…

Machine Learning · Computer Science 2020-09-03 Junyi Li , Bin Gu , Heng Huang

We propose a bilevel optimization strategy for selecting the best hyperparameter value for the nonsmooth $\ell_p$ regularizer with $0<p\le 1$. The concerned bilevel optimization problem has a nonsmooth, possibly nonconvex,…

Optimization and Control · Mathematics 2021-12-20 Takayuki Okuno , Akiko Takeda , Akihiro Kawana , Motokazu Watanabe

In this paper, we introduce the Hessian-Schatten total variation (HTV) -- a novel seminorm that quantifies the total "rugosity" of multivariate functions. Our motivation for defining HTV is to assess the complexity of supervised-learning…

Machine Learning · Computer Science 2022-02-01 Shayan Aziznejad , Joaquim Campos , Michael Unser

Image restoration is one of the most fundamental issues in imaging science. Total variation (TV) regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well…

Computer Vision and Pattern Recognition · Computer Science 2013-10-22 Jun Liu , Ting-Zhu Huang , Ivan W. Selesnick , Xiao-Guang Lv , Po-Yu Chen

Support vector classification (SVC) is a classical and well-performed learning method for classification problems. A regularization parameter, which significantly affects the classification performance, has to be chosen and this is usually…

Optimization and Control · Mathematics 2021-10-06 Qingna Li , Zhen Li , Alain Zemkoho