Almost Lossless Analog Signal Separation

We propose an information-theoretic framework for analog signal separation. Specifically, we consider the problem of recovering two analog signals from a noiseless sum of linear measurements of the signals. Our framework is inspired by the groundbreaking work of Wu and Verd\'u (2010) on almost lossless analog compression. The main results of the present paper are a general achievability bound for the compression rate in the analog signal separation problem, an exact expression for the optimal compression rate in the case of signals that have mixed discrete-continuous distributions, and a new technique for showing that the intersection of generic subspaces with subsets of sufficiently small Minkowski dimension is empty. This technique can also be applied to obtain a simplified proof of a key result in Wu and Verd\'u (2010).Comment: To be presented at IEEE Int. Symp. Inf. Theory 2013, Istanbul, Turke

A Deep Primal-Dual Network for Guided Depth Super-Resolution

In this paper we present a novel method to increase the spatial resolution of depth images. We combine a deep fully convolutional network with a non-local variational method in a deep primal-dual network. The joint network computes a noise-free, high-resolution estimate from a noisy, low-resolution input depth map. Additionally, a high-resolution intensity image is used to guide the reconstruction in the network. By unrolling the optimization steps of a first-order primal-dual algorithm and formulating it as a network, we can train our joint method end-to-end. This not only enables us to learn the weights of the fully convolutional network, but also to optimize all parameters of the variational method and its optimization procedure. The training of such a deep network requires a large dataset for supervision. Therefore, we generate high-quality depth maps and corresponding color images with a physically based renderer. In an exhaustive evaluation we show that our method outperforms the state-of-the-art on multiple benchmarks.Comment: BMVC 201

Toric complete intersections and weighted projective space

It has been shown by Batyrev and Borisov that nef partitions of reflexive polyhedra can be used to construct mirror pairs of complete intersection Calabi--Yau manifolds in toric ambient spaces. We construct a number of such spaces and compute their cohomological data. We also discuss the relation of our results to complete intersections in weighted projective spaces and try to recover them as special cases of the toric construction. As compared to hypersurfaces, codimension two more than doubles the number of spectra with $h^{11}=1$. Alltogether we find 87 new (mirror pairs of) Hodge data, mainly with $h^{11}\le4$.Comment: 16 pages, LaTeX2e, error in Hodge data correcte

High frequency microrheology with optical tweezers

textThis thesis presents a method to measure the linear viscoelastic response of fluids by tracking and analyzing the thermal, Brownian motion of suspended tracer particles, known as passive microrheology. The particle is confined in a harmonic optical trap and its one dimensional trajectory is obtained by a home-built split beam detection system, which works similar but responds faster than position detection with commercial quadrant photodiodes. The theory which is necessary to convert the particle trajectory into the complex shear modulus is derived in detail, pointing out that the commonly used Mason-Weitz method needs to be modified in order to obtain correct results at high frequencies due to hydrodynamic effects of the fluid. It follows a detailed explanation of the data analysis procedure which is verified for water up to angular frequencies of 10⁷ rad/s in very good agreement with the theory. Finally, there is an outlook how to apply the method to actual complex fluids.Physic

Completion of Matrices with Low Description Complexity

We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices encompassed by the theory is measured in terms of Hausdorff and upper Minkowski dimensions. Our goal is the characterization of the number of linear measurements, with an emphasis on rank-$1$ measurements, needed for the existence of an algorithm that yields reconstruction, either perfect, with probability 1, or with arbitrarily small probability of error, depending on the setup. Concretely, we show that matrices taken from a set $\mathcal{U}$ such that $\mathcal{U}-\mathcal{U}$ has Hausdorff dimension $s$ can be recovered from $k>s$ measurements, and random matrices supported on a set $\mathcal{U}$ of Hausdorff dimension $s$ can be recovered with probability 1 from $k>s$ measurements. What is more, we establish the existence of recovery mappings that are robust against additive perturbations or noise in the measurements. Concretely, we show that there are $\beta$-H\"older continuous mappings recovering matrices taken from a set of upper Minkowski dimension $s$ from $k>2s/(1-\beta)$ measurements and, with arbitrarily small probability of error, random matrices supported on a set of upper Minkowski dimension $s$ from $k>s/(1-\beta)$ measurements. The numerous concrete examples we consider include low-rank matrices, sparse matrices, QR decompositions with sparse R-components, and matrices of fractal nature

Within-ring movement of free water in dehydrating Norway spruce sapwood visualized by neutron radiography

This study is a first approach to visualize moisture distribution and movement between annual rings during sapwood drying by neutron imaging (NI). While Norway spruce [Picea abies (L.) Karst.] sapwood beams were allowed to dehydrate on a balance at ambient conditions, NI was performed in 1-10 min time steps. From NI raw files, radial dimensional changes were calculated during dehydration and transmission profiles were drawn for different relative moisture content (MC) steps from full saturation until equilibrium moisture content. The NI technique proved to be a useful tool to visualize the movement of free water within, and between, annual rings. Removal of free water in the middle part of the wood beam did not proceed continuously from the surface to the central part, but was strongly influenced by wood anatomy. Water is removed from earlywood during early stages of dehydration and later, at higher moisture loss (<50% MC), from the main latewood parts. It is therefore concluded that the radial dimensional changes measured at moderate moisture loss are not only caused by cell wall shrinkage of the outer wood parts located beneath the wood surface, but a result of elastic deformation of earlywood tracheids under the influence of negative hydrostatic pressure