The factorization method for inverse scattering from periodic inhomogeneous media

This book addresses the identification of the shape of penetrable periodic media by means of scattered time-harmonic waves. Mathematically, this is about the determination of the support of a function which occurs in the governing equations. Our theoretical analysis shows that this problem can be strictly solved for acoustic as well as for electromagnetic radiation by the so-called Factorization Method. We apply this method to reconstruct a couple of media from numerically simulated field data

Analysing Ewald\u27s Method for the Evaluation of Green\u27s Functions for Periodic Media

Expressions for periodic Green\u27s functions for the Helmholtz equation in two and three dimensions are derived via Ewald\u27s method. The decay rate of the series occurring in these expressions is analysed and rigorous estimates for the remainder are derived when the series are truncated and replaced by finite sums. The effect of choosing a control parameter occurring in Ewald\u27s expressions is discussed and some recommendations for its choice are given based on the aforementioned estimates. We present various numerical examples for the resulting method for evaluating the Green\u27s functions. The results can also be carried over to evaluating the partial derivatives

Improving Marlin's compression ratio with partially overlapping codewords

Marlin [1] is a Variable-to-Fixed (VF) codec optimized for decoding speed. To achieve its speed, Marlin does not encode the current state of the input source, penalyzing compression ratio. In this paper we address this penalty by partially encoding the current state of the input in the lower bits of the codeword. Those bits select which chapter in the dictionary must be used to decode the next codeword. Each chapter is specialized for a subset of states, improving compression ratio. At the same time, we use one victim chapter to encode all rare symbols, increasing the efficiency of the rest of them. The decoding algorithm remains the same, only now codewords have overlapping bits. Mapping techniques allow us to combine common chapters and thus keep an efficient use of the L1 cache. We evaluate our approach with both synthetic and real data sets, and show significant improvements in low entropy sources, where compression efficiency can improve from 93.9% to 98.6%

The factorization method for inverse scattering from periodic inhomogeneous media

This book addresses the identification of the shape of penetrable periodic media by means of scattered time-harmonic waves. Mathematically, this is about the determination of the support of a function which occurs in the governing equations. Our theoretical analysis shows that this problem can be strictly solved for acoustic as well as for electromagnetic radiation by the so-called Factorization Method. We apply this method to reconstruct a couple of media from numerically simulated field data

LABELING OF N-DIMENSIONAL IMAGES WITH CHOOSABLE ADJACENCY OF THE PIXELS

The labeling of discretized image data is one of the most essential operations in digital image processing. The notions of an adjacency system of pixels and the complementarity of two such systems are crucial to guarantee consistency of any labeling routine. In to date's publications, this complementarity usually is defined using discrete versions of the Jordan-Veblen curve theorem and the Jordan-Brouwer surface theorem for 2D and 3D images, respectively. In contrast, we follow here an alternative concept, which relies on a consistency relation for the Euler number. This relation and all necessary definitions are easily stated in a uniform manner for the n-dimensional case. For this, we present identification and convergence results for complementary adjacency systems, supplemented by examples for the 3D case. Next, we develop a pseudo-code for a general labeling algorithm. The application of such an algorithm should be assessed with regard to our preceding considerations. A benchmark and a thorough discussion finish our article

Improving Marlin's compression ratio with partially overlapping codewords

Marlin [1] is a Variable-to-Fixed (VF) codec optimized for decoding speed. To achieve its speed, Marlin does not encode the current state of the input source, penalyzing compression ratio. In this paper we address this penalty by partially encoding the current state of the input in the lower bits of the codeword. Those bits select which chapter in the dictionary must be used to decode the next codeword. Each chapter is specialized for a subset of states, improving compression ratio. At the same time, we use one victim chapter to encode all rare symbols, increasing the efficiency of the rest of them. The decoding algorithm remains the same, only now codewords have overlapping bits. Mapping techniques allow us to combine common chapters and thus keep an efficient use of the L1 cache. We evaluate our approach with both synthetic and real data sets, and show significant improvements in low entropy sources, where compression efficiency can improve from 93.9% to 98.6%