AOLIP - Analysis Operator Learning for Image Processing

• Applicant: Professor Dr.-Ing. Klaus Diepold, since 8/2016
• Subject Area: Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing
• Term: from 2013 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 246651110

Exploiting structure in data is crucial for the success of many techniques in machine learning and image processing, and sparse data models have been playing a significant role. As a consequence, sparsity has become a very active field of research with numerous algorithms proposed within the machine learning and signal processing communities over the last few years. These methods either aim at finding sparse representations of data or at exploiting sparsity in these models.In contrast to the well-established synthesis model, also known as sparse coding, considerably less attention has been drawn to an interesting alternative, the so called co-sparse analysis model. Herein, an analysis operator linearly maps the data to a higher dimensional space, while the image of this mapping is enforced to be sparse. Recent work reveals that the analysis approach can outperform the synthesis approach in regularizing inverse problems and it has particularly proven useful in imaging applications.In order to design effective learning algorithms, a solid theory has to be established and the developed methods need to be evaluated properly. While theoretical results on the structure of optimal synthesis dictionaries have been presented, the analysis model is far from being fully understood and many applications lack comparable results. For example, in imaging the literature lacks a rigorous theoretical analysis that examines under which conditions on the operator and the signal the recovery success is guaranteed. For other data analysis tasks such as feature extraction and multidimensional image data analysis even fewer results exist.The goal of this proposal is to answer some crucial theoretical questions and to further explore this promising field of research in order to fill the gaps in the theory and to further drive the development of the co-sparse analysis model as a generic tool for image analysis.We will investigate the sample complexity for learning an analysis operator together with a local stability analysis of common learning procedures. These learning procedures will be extended to cope with multi-dimensional image data, as e.g. color images or 3D image data. Furthermore, we will introduce a separable structure on the learned operators. Such an extension can lead to a gain in performance in terms of computational complexity and the ability to handle high-dimensional data. Furthermore, the project will explore the relation of the co-sparse analysis model to sparse auto-encoders, which are very successful in the context of deep learning architectures. Considering the problem of image reconstruction, we will finally investigate algorithms that blindly learn a co-sparse analysis model jointly with solving the reconstruction task.

• DFG Programme: Research Grants
• Ehemaliger Antragsteller: Professor Dr. Martin Kleinsteuber, until 8/2016