TY - GEN A1 - Hoeltgen, Laurent A1 - Peter, Pascal A1 - Breuß, Michael T1 - Clustering-based quantisation for PDE-based image compression T2 - Signal, Image and Video Processing N2 - Optimal known pixel data for inpainting in compression codecs based on partial differential equations is real-valued and thereby expensive to store. Thus, quantisation is required for efficient encoding. In this paper, we interpret the quantisation step as a clustering problem. Due to the global impact of each known pixel and correlations between spatial and tonal data, we investigate the central question, which kind of feature vectors should be used for clustering with popular strategies such as k-means. Our findings show that the number of colours can be reduced significantly without impacting the reconstruction quality. Surprisingly, these benefits are negated by an increased coding cost in compression applications. KW - Laplace interpolation KW - Inpainting KW - Compression KW - Quantisation KW - Clustering KW - Partial differential equations Y1 - 2018 U6 - https://doi.org/10.1007/s11760-017-1173-9 SN - 1863-1703 SN - 1863-1711 VL - 12 IS - 3 SP - 411 EP - 419 ER - TY - GEN A1 - Hoeltgen, Laurent A1 - Breuß, Michael A1 - Herold, Gert A1 - Sarradj, Ennes T1 - Sparse ℓ1 regularisation of matrix valued models for acoustic source characterisation T2 - Optimization and Engineering N2 - We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears similarities to the basis pursuit formalism but also relies on additional model assumptions that are challenging from a mathematical point of view. Our approach reformulates the original task as a convex optimisation model. The sought solution shall be a matrix with a certain desired structure. We enforce this structure through additional constraints. By combining popular splitting algorithms and matrix differential theory in a novel framework we obtain a numerically efficient strategy. Besides a thorough theoretical consideration we also provide an experimental setup that certifies the usability of our strategy. Finally, we also address practical issues, such as the handling of inaccuracies in the measurement and corruption of the given data. We provide a post processing step that is capable of yielding an almost perfect solution in such circumstances. KW - Convex optimisation KW - Sparse recovery KW - Split Bregman KW - Microphone array KW - Matrix differentiation KW - Acoustic source characterisation Y1 - 2018 U6 - https://doi.org/10.1007/s11081-017-9357-2 SN - 1389-4420 SN - 1573-2924 VL - 19 IS - 1 SP - 39 EP - 70 ER - TY - CHAP A1 - Dachsel, Robert A1 - Breuß, Michael A1 - Hoeltgen, Laurent ED - Welk, Martin ED - Urschler, Martin ED - Roth, Peter M. T1 - A Study of Spectral Expansion for Shape Correspondence T2 - Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria N2 - The main task in three dimensional non-rigid shape correspondence is to retrieve similarities between two or more similar three dimensional objects. A useful way to tackle this problem is to construct a simplified shape representation, called feature descriptor, which is invariant under deformable transformations. A successful class of such feature descriptors is based on physical phenomena, concretely by the heat equation for the heat kernel signature and the Schrödinger equation for the wave kernel signature. Both approaches employ the spectral decomposition of the Laplace-Beltrami operator, meaning that solutions of the corresponding equations are expressed by a series expansion in terms of eigenfunctions. The feature descriptor is then computed at hand of those solutions. In this paper we explore the influence of the amount of used eigenfunctions on shape correspondence applications, as this is a crucial point with respect to accuracy and overall computational efficiency of the method. Our experimental study will be performed at hand of a standard shape data set. Y1 - 2018 SN - 978-3-85125-603-1 U6 - https://doi.org/10.3217/978-3-85125-603-1-15 SP - 73 EP - 79 PB - Verlag der TU Graz CY - Graz ER -