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Publications in the field of Signal Denoising and Reconstruction

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2015

  Learning fast and effective image restoration models paper              
  Yunjin Chen       PhD Thesis  
paper Up to now, image restoration remains an active research topic, and many new approaches are constantly emerging. However, many newly proposed algorithms achieve the state-of-the-art performance, at the expense of computation time. The goal of this thesis is to develop effective image restoration approaches with both high computational efficiency and recovery quality. To that end, we focus on variational models and some related models derived from them, e.g., nonlinear diffusion processes, due to their effectiveness for many generally ill-posed computer vision problems...
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  On learning optimized reaction diffusion processes for effective image restoration paper       software   links  
  Yunjin Chen, Wei Yu, Thomas Pock       CVPR 2015  
paper For several decades, image restoration remains an active research topic in low-level computer vision and hence new approaches are constantly emerging. However, many recently proposed algorithms achieve state-of-the-art performance only at the expense of very high computation time, which clearly limits their practical relevance. In this work, we propose a simple but effective approach with both high computational efficiency and high restoration quality. We extend conventional nonlinear reaction diffusion models by several parametrized linear filters as well as several parametrized influence functions.
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2014

  A higher-order MRF based variational model for multiplicative noise reduction paper       software      
  Yunjin Chen, Wensen Feng, Rene Ranftl, Hong Qiao, Thomas Pock       IEEE Signal Processing Letters  
paper The Fields of Experts (FoE) image prior model, a filter-based higher-order Markov Random Fields (MRF) model, has been shown to be effective for many image restoration problems. Motivated by the successes of FoE-based approaches, in this letter we propose a novel variational model for multiplicative noise reduction based on the FoE image prior model. The resulting model corresponds to a non-convex minimization problem, which can be efficiently solved by a recently published non-convex optimization algorithm.
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  Insights into analysis operator learning: From patch-based sparse models to higher-order MRFs paper       software      
  Yunjin Chen, Rene Ranftl, Thomas Pock       Preprint  
paper This paper addresses a new learning algorithm for the recently introduced co-sparse analysis model. First, we give new insights into the co-sparse analysis model by establishing connections to filter-based MRF models, such as the Field of Experts (FoE) model of Roth and Black. For training, we introduce a technique called bi-level optimization to learn the analysis operators. Compared to existing analysis operator learning approaches, our training procedure has the advantage that it is unconstrained with respect to the analysis operator.
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2013

  A Convex, Lower Semi-Continuous Approximation of Euler's Elastica energy paper              
  Kristian Bredies, Thomas Pock, Benedikt Wirth       Preprint  
paper We propose a convex, lower semi-continuous, coercive approximation of Euler's elastica energy for images, which is thus very well-suited as a regularizer in image processing. The approximation is not quite the convex relaxation, and we discuss its close relation to the exact convex relaxation as well as the difficulties associated with computing the latter. Interestingly, the convex relaxation of the elastica energy reduces to constantly zero if the total variation part of the elastica energy is neglected.
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  A Convex Approach for Image Hallucination paper       software      
  Peter Innerhofer, Thomas Pock       OAGM/AAPR Workshop 2013  
paper In this paper we propose a global convex approach for image hallucination. Altering the idea of classical multi image super resolution (SU) systems to single image SU, we incorporate aligned images to hallucinate the output. Our work is based on the paper of Tappen et al. where they use a non-convex model for image hallucination. In comparison we formulate a convex primal optimization problem and derive a fast converging primal-dual algorithm with a global optimal solution.
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  Revisiting loss-specific training of filter-based MRFs for image restoration paper       software      
  Yunjin Chen, Thomas Pock, Rene Ranftl, Horst Bischof       GCPR 2013  
paper It is now well known that Markov random fields (MRFs) are particularly effective for modeling image priors in low-level vision. Recent years have seen the emergence of two main approaches for learning the parameters in MRFs: (1) probabilistic learning using sampling-based algorithms and (2) loss-specific training based on MAP estimate. After investigating existing training approaches, it turns out that the performance of the loss-specific training has been significantly underestimated in existing work.
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  An iterated l1 Algorithm for Non-smooth Non-convex Optimization in Computer Vision paper              
  Peter Ochs, Alexey Dosovitskiy, Thomas Brox, Thomas Pock       CVPR 2013  
paper Natural image statistics indicate that we should use non-convex norms for most regularization tasks in image processing and computer vision. Still, they are rarely used in practice due to the challenge to optimize them. Recently, iteratively reweighed l1 minimization has been proposed as a way to tackle a class of non-convex functions by solving a sequence of convex l2 - l1 problems. Here we extend the problem class to linearly constrained optimization of a Lipschitz continuous function, which is the sum of a convex function and a function being concave and increasing on the non-negative orthant (possibly non-convex and non-concave on the whole space).
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2012

  Learning l1-based analysis and synthesis sparsity priors using bi-level optimization paper              
  Yunjin Chen, Thomas Pock, Horst Bischof       Workshop on Analysis Operator Learning vs. Dictionary Learning, NIPS 2012  
paper We consider the analysis operator and synthesis dictionary learning problems based on the the l1 regularized sparse representation model. We reveal the internal relations between the l1 -based analysis model and synthesis model. We then introduce an approach to learn both analysis operator and synthesis dictionary simultaneously by using a unified framework of bi-level optimization. Our aim is to learn a meaningful operator (dictionary) such that the minimum energy solution of the analysis (synthesis)-prior based model is as close as possible to the groundtruth.
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  A bilevel optimization approach for parameter learning in variational models paper              
  Karl Kunisch, Thomas Pock       SIAM Journal on Imaging Sciences  
paper In this work we consider the problem of parameter learning for variational image denoising models. The learning problem is formulated as a bilevel optimization problem, where the lower level problem is given by the variational model and the higher level problem is expressed by means of a loss function that penalizes errors between the solution of the lower level problem and the ground truth data. We consider a class of image denoising models incorporating p -norm based analysis priors using a fixed set of linear operators.
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  Convex relaxation of a class of vertex penalizing functionals paper              
  Kristian Bredies, Thomas Pock, Benedikt Wirth       Journal of Mathematical Imaging and Vision  
paper We investigate a class of variational problems that incorporate in some sense curvature information of the level lines. The functionals we consider incorporate metrics defined on the orientations of pairs of line segments that meet in the vertices of the level lines. We discuss two particular instances: One instance that minimizes the total number of vertices of the level lines and another instance that minimizes the total sum of the absolute exterior angles between the line segments.
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2010

  A Convex Approach for Variational Super-Resolution paper              
  Markus Unger and Thomas Pock and Manuel Werlberger and Horst Bischof       DAGM 2010, Annual Symposium of the German Association for Pattern Recognition  
paper We propose a convex variational framework to compute high resolution images from a low resolution video. The image formation process is analyzed to provide to a well designed model for warping, blurring, downsampling and regularization. We provide a comprehensive investigation of the single model components. The super-resolution problem is modeled as a minimization problem in an unified convex framework...
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  Exploiting Redundancy for Aerial Image Fusion using Convex Optimization paper              
  Stefan Kluckner and Thomas Pock and Horst Bischof       DAGM 2010, Annual Symposium of the German Association for Pattern Recognition  
paper This paper proposes a variational formulation for a tight integration of redundant image data showing urban environments. We introduce an efficient wavelet regularization which enables a natural-appearing recovery of fine details in the images by performing joint inpainting and denoising from a given set of input observations ...
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  Fast reduction of undersampling artifacts in radial MR angiography with 3D total variation on graphics hardware paper              
  Florian Knoll and Markus Unger and Clemens Diwoky and Christian Clason and Thomas Pock and Rudolf Stollberger       Magnetic Resonance Materials in Physics, Biology and Medicine  
paper Objective Subsampling of radially encoded MRI acquisitions in combination with sparsity promoting methods opened a door to significantly increased imaging speed, which is crucial for many important clinical applications. In particular, it has been shown recently that total variation (TV) regularization ef?ciently reduces undersampling artifacts...
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  Total Generalized Variation paper              
  Kristian Bredies, Karl Kunisch, Thomas Pock       Accepted to SIIMS  
paper The novel concept of total generalized variation of a function u is introduced and some of its essential properties are proved. Differently from the bounded variation semi-norm, the new concept involves higher order derivatives of u. Numerical examples illustrate the high quality of this functional as a regularization term for mathematical imaging problems...
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  Global Solutions of Variational Models with Convex Regularization paper              
  Thomas Pock, Daniel Cremers, Horst Bischof, Antonin Chambolle       Accepted to SIIMS  
paper We propose an algorithmic framework to compute global solutions of variational models with convex regularity terms that permit quite arbitrary data terms. While the minimization of variational problems with convex data and regularity terms is straight forward (using for example gradient descent), this is no longer trivial for functionals with non-convex data terms...
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2009

  An Introduction to Total Variation for Image Analysis paper           links  
  Antonin Chambolle, Vicent Caselles, Matteo Novaga, Daniel Cremers, Thomas Pock       Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery", 2009, Linz, Austria  
paper These are the lecture notes of a course taught in Linz in Sept., 2009, at the school "Theoretical Foundations and Numerical Methods for Sparse Recovery", organized by Massimo Fornasier and Ronny Romlau. They address various theoretical and practical topics...
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  A Variational Approach to Semiautomatic Generation of Digital Terrain Models paper              
  Markus Unger, Thomas Pock, Markus Grabner, Andreas Klaus, Horst Bischof       5th Int. Symp. on Visual Computing, Las Vegas, USA  
paper We present a semiautomatic approach to generate high quality digital terrain models (DTM) from digital surface models (DSM). A DTM is a model of the earths surface, where all man made objects and the vegetation have been removed. In order to achieve this, we use a variational energy minimization approach. The proposed energy functional incorporates Huber regularization to yield piecewise smooth surfaces...
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  Video Super Resolution using Duality Based TV-L1 Optical Flow paper              
  Dennis Mitzel, Thomas Pock, Thomas Schoenemann, Daniel Cremers       DAGM 2009  
paper In this paper, we propose a variational framework for computing a superresolved image of a scene from an arbitrary input video. To this end, we employ a recently proposed quadratic relaxation scheme for high accuracy optic flow estimation. Subsequently we estimate a high resolution image using a variational approach...
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  An Algorithm for Minimizing the Mumford-Shah Functional paper              
  Thomas Pock, Daniel Cremers, Horst Bischof, Antonin Chambolle       International Conference on Computer Vision 2009  
paper In this work we revisit the Mumford-Shah functional, one of the most studied variational approaches to image segmentation. The contribution of this paper is to propose an algorithm which allows to minimize a convex relaxation of the Mumford-Shah functional obtained by functional lifting. The algorithm is an efficient primal-dual projection algorithm for which we prove convergence.
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2008

  Real Time Elimination of Undersampling Artifacts in CE MRA using Variational Denoising on Graphics Hardware paper              
  Florian Knoll, Markus Unger, Franz Ebner, Rudolf Stollberger       20th Annual Int. Conference on Magnetic Resonance Angiography  
paper Undersampled imaging strategies with state of the art reconstruction methods like compressed sensing, which reformulate image reconstruction as a constrained optimization problem, have the potential to deliver CE MRA images with high spatial and temporal resolution. The drawback...
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  Fast Total Variation for Computer Vision paper              
  Thomas Pock       Phd Thesis 2008  
paper Motivated by statistical inference methods, variational methods are among the most successful methods to solve a number of different Computer Vision problems. Variational methods aim to minimize an energy functional...
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2007

  Real-time Computation of Variational Methods on Graphics Hardware paper              
  Thomas Pock, Markus Grabner, Horst Bischof       Computer Vision Winter Workshop 2007  
paper This paper combines two powerful approaches: variational methods and graphics hardware. Variational methods have demonstrated considerable success in computer vision for such diverse tasks as denoising, segmentation, registration, stereo matching...
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