arXiv subjects

Thomas Pock

Publications and source records attributed to Thomas Pock.

77 records · Page 5Linked to original sources

arXiv2014

Learning $\ell_1$-based analysis and synthesis sparsity priors using bi-level optimization

We consider the analysis operator and synthesis dictionary learning problems based on the the $\ell_1$ regularized sparse representation model. We reveal the internal relations between the $\ell_1$-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 ground-truth. We solve the bi-level optimization problem using the implicit differentiation technique. Moreover, we demonstrate the effectiveness of our leaning approach by applying the learned analysis operator (dictionary) to the image denoising task and comparing its performance with state-of-the-art methods. Under this unified framework, we can compare the performance of the two types of priors.

cs.CV↗

arXiv2014

Revisiting loss-specific training of filter-based MRFs for image restoration

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. In this paper, we revisit this approach and use techniques from bi-level optimization to solve it. We show that we can get a substantial gain in the final performance by solving the lower-level problem in the bi-level framework with high accuracy using our newly proposed algorithm. As a result, our trained model is on par with highly specialized image denoising algorithms and clearly outperforms probabilistically trained MRF models. Our findings suggest that for the loss-specific training scheme, solving the lower-level problem with higher accuracy is beneficial. Our trained model comes along with the additional advantage, that inference is extremely efficient. Our GPU-based implementation takes less than 1s to produce state-of-the-art performance.

cs.CV↗

arXiv2014

Insights into analysis operator learning: From patch-based sparse models to higher-order MRFs

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. We investigate the effect of different aspects of the co-sparse analysis model and show that the sparsity promoting function (also called penalty function) is the most important factor in the model. In order to demonstrate the effectiveness of our training approach, we apply our trained models to various classical image restoration problems. Numerical experiments show that our trained models clearly outperform existing analysis operator learning approaches and are on par with state-of-the-art image denoising algorithms. Our approach develops a framework that is intuitive to understand and easy to implement.

cs.CV↗

arXiv2013

Filament and Flare Detection in Hα image sequences

Solar storms can have a major impact on the infrastructure of the earth. Some of the causing events are observable from ground in the Hα spectral line. In this paper we propose a new method for the simultaneous detection of flares and filaments in Hα image sequences. Therefore we perform several preprocessing steps to enhance and normalize the images. Based on the intensity values we segment the image by a variational approach. In a final postprecessing step we derive essential properties to classify the events and further demonstrate the performance by comparing our obtained results to the data annotated by an expert. The information produced by our method can be used for near real-time alerts and the statistical analysis of existing data by solar physicists.

cs.CV↗

arXiv2013

A Convex Approach for Image Hallucination

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. We use a database with face images to incorporate high-frequency details to the high-resolution output. We show that we can achieve state-of-the-art results by using a convex approach.

cs.CV↗