A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...

/pdf/the-empirical-mode-decomposition-and-the-hilbert-spectrum-qkmom366dy.pdf

The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

The time-frequency and time-scale communities have recently developed a large number of overcomplete waveform dictionaries --- stationary wavelets, wavelet packets, cosine packets, chirplets, and warplets, to name a few. Decomposition into overcomplete systems is not unique, and several methods for decomposition have been proposed, including the method of frames (MOF), Matching pursuit (MP), and, for special dictionaries, the best orthogonal basis (BOB).
Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions. We give examples exhibiting several advantages over MOF, MP, and BOB, including better sparsity and superresolution. BP has interesting relations to ideas in areas as diverse as ill-posed problems, in abstract harmonic analysis, total variation denoising, and multiscale edge denoising.
BP in highly overcomplete dictionaries leads to large-scale optimization problems. With signals of length 8192 and a wavelet packet dictionary, one gets an equivalent linear program of size 8192 by 212,992. Such problems can be attacked successfully only because of recent advances in linear programming by interior-point methods. We obtain reasonable success with a primal-dual logarithmic barrier method and conjugate-gradient solver.

Atomic Decomposition by Basis Pursuit

The self-organized map, an architecture suggested for artificial neural networks, is explained by presenting simulation experiments and practical applications. The self-organizing map has the property of effectively creating spatially organized internal representations of various features of input signals and their abstractions. One result of this is that the self-organization process can discover semantic relationships in sentences. Brain maps, semantic maps, and early work on competitive learning are reviewed. The self-organizing map algorithm (an algorithm which order responses spatially) is reviewed, focusing on best matching cell selection and adaptation of the weight vectors. Suggestions for applying the self-organizing map algorithm, demonstrations of the ordering process, and an example of hierarchical clustering of data are presented. Fine tuning the map by learning vector quantization is addressed. The use of self-organized maps in practical speech recognition and a simulation experiment on semantic mapping are discussed. >

The self-organizing map

In this paper, we compare the performance of descriptors computed for local interest regions, as, for example, extracted by the Harris-Affine detector [Mikolajczyk, K and Schmid, C, 2004]. Many different descriptors have been proposed in the literature. It is unclear which descriptors are more appropriate and how their performance depends on the interest region detector. The descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector. Our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations. We compare shape context [Belongie, S, et al., April 2002], steerable filters [Freeman, W and Adelson, E, Setp. 1991], PCA-SIFT [Ke, Y and Sukthankar, R, 2004], differential invariants [Koenderink, J and van Doorn, A, 1987], spin images [Lazebnik, S, et al., 2003], SIFT [Lowe, D. G., 1999], complex filters [Schaffalitzky, F and Zisserman, A, 2002], moment invariants [Van Gool, L, et al., 1996], and cross-correlation for different types of interest regions. We also propose an extension of the SIFT descriptor and show that it outperforms the original method. Furthermore, we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the SIFT-based descriptors perform best. Moments and steerable filters show the best performance among the low dimensional descriptors.

/pdf/a-performance-evaluation-of-local-descriptors-3nm3px4c9t.pdf

A performance evaluation of local descriptors

Theory of communication

IT is known that the spherical aberration of electron lenses sets a limit to the resolving power of electron microscopes at about 5 A. Suggestions for the correction of objectives have been made ; but these are difficult in themselves, and the prospects of improvement are further aggravated by the fact that the resolution limit is proportional to the fourth root of the spherical aberration. Tnus an improvement of the resolution by one decimal wotild require a correction of the objective to four decimals, a practically hopeless task.

/pdf/a-new-microscopic-principle-2a06oi3wvh.pdf

A new microscopic principle.

The subject of this paper is a new two-step method of optical imagery. In a first step the object is illuminated with a coherent monochromatic wave, and the diffraction pattern resulting from the interference of the coherent secondary wave issuing from the object with the strong, coherent background is recorded on a photographic plate. If the photographic plate, suitably processed, is replaced in the original position and illuminated with the coherent background alone, an image of the object will appear behind it, in the original position. It is shown that this process reconstructs the coherent secondary wave, together with an equally strong ‘twin wave’ which has the same amplitude, but opposite phase shifts relative to the background. The illuminating wave itself can be used for producing the coherent background. The simplest case is illumination by a point source. In this case the two twin waves are shown to correspond to two ‘twin objects’, one of which is the original, while the other is its mirror image with respect to the illuminating centre. A physical aperture can be used as a point source, or the image of an aperture produced by a condenser system . If this system has aberrations, such as astigmatism or spherical aberration, the twin image will be no longer sharp but will appear blurred, as if viewed through a system with twice the aberrations of the condenser. In either case the correct image of the object can be effectively isolated from its twin, and separately observed. Three-dimensional objects can be reconstructed, as well as two-dimensional. The wave used in the reconstruction need not be the original, it can be, for example, a light-optical imitation of the electron wave with which the diffraction diagram was taken. Thus it becomes possible to extend the idea of Sir Lawrence Bragg’s ‘X -ray microscope’ to arbitrary objects, and use the new method for improvements in electron microscopy. The apparatus will consist of two parts, an electronic device in which a diffraction pattern is taken with electrons diverging from a fine focus, and an optical synthetizer, which imitates the essential data of the electronic device on a much enlarged scale. The theory of the analysis-synthesis cycle is developed, with a discussion of the impurities arising in the reconstruction, and their avoidance. The limitations of the new method are due chiefly to the small intensities which are available in coherent beams, but it appears perfectly feasible to achieve a resolution limit of 1 A, ultimately perhaps even better.

/pdf/microscopy-by-reconstructed-wave-fronts-1o7qb4esj3.pdf

Microscopy by reconstructed wave-fronts

IN popular expositions of wave mechanics, acoustical illustrations have been used by several authors, with particular success by Lande1. In a recent paper on the “Theory of Communication”2 I have taken the opposite course. Acoustical phenomena are discussed by mathematical methods closely related to those of quantum theory. While in physical acoustics a new formal approach to old problems cannot be expected to reveal much that is not already known, the position in subjective acoustics is rather different. In fact, the new methods have already proved their heuristic value, and can be expected to throw more light on the theory of hearing. In my original paper the point of view was mainly that of communication engineering ; in the following survey I have emphasized those features which may be of interest to physicists and to physiologists.

Dennis Gabor

Papers

Theory of communication

A new microscopic principle.

Microscopy by reconstructed wave-fronts

Acoustical quanta and the theory of hearing.

Inventing the Future