2,389 research outputs found
Wavelets, ridgelets and curvelets on the sphere
We present in this paper new multiscale transforms on the sphere, namely the
isotropic undecimated wavelet transform, the pyramidal wavelet transform, the
ridgelet transform and the curvelet transform. All of these transforms can be
inverted i.e. we can exactly reconstruct the original data from its
coefficients in either representation. Several applications are described. We
show how these transforms can be used in denoising and especially in a Combined
Filtering Method, which uses both the wavelet and the curvelet transforms, thus
benefiting from the advantages of both transforms. An application to component
separation from multichannel data mapped to the sphere is also described in
which we take advantage of moving to a wavelet representation.Comment: Accepted for publication in A&A. Manuscript with all figures can be
downloaded at http://jstarck.free.fr/aa_sphere05.pd
ENO-wavelet transforms for piecewise smooth functions
We have designed an adaptive essentially nonoscillatory (ENO)-wavelet transform for approximating discontinuous functions without oscillations near the discontinuities. Our approach is to apply the main idea from ENO schemes for numerical shock capturing to standard wavelet transforms. The crucial point is that the wavelet coefficients are computed without differencing function values across jumps. However, we accomplish this in a different way than in the standard ENO schemes. Whereas in the standard ENO schemes the stencils are adaptively chosen, in the ENO-wavelet transforms we adaptively change the function and use the same uniform stencils. The ENO-wavelet transform retains the essential properties and advantages of standard wavelet transforms such as concentrating the energy to the low frequencies, obtaining maximum accuracy, maintained up to the discontinuities, and having a multiresolution framework and fast algorithms, all without any edge artifacts. We have obtained a rigorous approximation error bound which shows that the error in the ENO-wavelet approximation depends only on the size of the derivative of the function away from the discontinuities. We will show some numerical examples to illustrate this error estimate
Denosing Using Wavelets and Projections onto the L1-Ball
Both wavelet denoising and denosing methods using the concept of sparsity are
based on soft-thresholding. In sparsity based denoising methods, it is assumed
that the original signal is sparse in some transform domains such as the
wavelet domain and the wavelet subsignals of the noisy signal are projected
onto L1-balls to reduce noise. In this lecture note, it is shown that the size
of the L1-ball or equivalently the soft threshold value can be determined using
linear algebra. The key step is an orthogonal projection onto the epigraph set
of the L1-norm cost function.Comment: Submitted to Signal Processing Magazin
NMDA-based pattern discrimination in a modeled cortical neuron
Compartmental simulations of an anatomically characterized cortical pyramidal cell were carried out to study the integrative behavior of a complex dendritic tree. Previous theoretical (Feldman and Ballard 1982; Durbin and Rumelhart 1989; Mel 1990; Mel and Koch 1990; Poggio and Girosi 1990) and compartmental modeling (Koch et al. 1983; Shepherd et al. 1985; Koch and Poggio 1987; Rall and Segev 1987; Shepherd and Brayton 1987; Shepherd et al. 1989; Brown et al. 1991) work had suggested that multiplicative interactions among groups of neighboring synapses could greatly enhance the processing power of a neuron relative to a unit with only a single global firing threshold. This issue was investigated here, with a particular focus on the role of voltage-dependent N-methyl-D-asparate (NMDA) channels in the generation of cell responses. First, it was found that when a large proportion of the excitatory synaptic input to dendritic spines is carried by NMDA channels, the pyramidal cell responds preferentially to spatially clustered, rather than random, distributions of activated synapses. Second, based on this mechanism, the NMDA-rich neuron is shown to be capable of solving a nonlinear pattern discrimination task. We propose that manipulation of the spatial ordering of afferent synaptic connections onto the dendritic arbor is a possible biological strategy for pattern information storage during learning
The IPRS Image Processing and Pattern Recognition System.
IPRS is a freely available software system which consists of about 250 library functions in C, and a set of application programs. It is designed to run under UNIX and comes with full source code, system manual pages, and a comprehensive user's and programmer's guide. It is intended for use by researchers in human vision, pattern recognition, image processing, machine vision and machine learning
Vision-Based Road Detection in Automotive Systems: A Real-Time Expectation-Driven Approach
The main aim of this work is the development of a vision-based road detection
system fast enough to cope with the difficult real-time constraints imposed by
moving vehicle applications. The hardware platform, a special-purpose massively
parallel system, has been chosen to minimize system production and operational
costs. This paper presents a novel approach to expectation-driven low-level
image segmentation, which can be mapped naturally onto mesh-connected massively
parallel SIMD architectures capable of handling hierarchical data structures.
The input image is assumed to contain a distorted version of a given template;
a multiresolution stretching process is used to reshape the original template
in accordance with the acquired image content, minimizing a potential function.
The distorted template is the process output.Comment: See http://www.jair.org/ for any accompanying file
Two-photon imaging and analysis of neural network dynamics
The glow of a starry night sky, the smell of a freshly brewed cup of coffee
or the sound of ocean waves breaking on the beach are representations of the
physical world that have been created by the dynamic interactions of thousands
of neurons in our brains. How the brain mediates perceptions, creates thoughts,
stores memories and initiates actions remains one of the most profound puzzles
in biology, if not all of science. A key to a mechanistic understanding of how
the nervous system works is the ability to analyze the dynamics of neuronal
networks in the living organism in the context of sensory stimulation and
behaviour. Dynamic brain properties have been fairly well characterized on the
microscopic level of individual neurons and on the macroscopic level of whole
brain areas largely with the help of various electrophysiological techniques.
However, our understanding of the mesoscopic level comprising local populations
of hundreds to thousands of neurons (so called 'microcircuits') remains
comparably poor. In large parts, this has been due to the technical
difficulties involved in recording from large networks of neurons with
single-cell spatial resolution and near- millisecond temporal resolution in the
brain of living animals. In recent years, two-photon microscopy has emerged as
a technique which meets many of these requirements and thus has become the
method of choice for the interrogation of local neural circuits. Here, we
review the state-of-research in the field of two-photon imaging of neuronal
populations, covering the topics of microscope technology, suitable fluorescent
indicator dyes, staining techniques, and in particular analysis techniques for
extracting relevant information from the fluorescence data. We expect that
functional analysis of neural networks using two-photon imaging will help to
decipher fundamental operational principles of neural microcircuits.Comment: 36 pages, 4 figures, accepted for publication in Reports on Progress
in Physic
A Greedy Algorithm for a Sparse Scalet Decomposition
International audienceSparse decompositions were mainly developed to optimize the signal or the image compression. The sparsity was first obtained by a coefficient thresholding. The matching pursuit (MP) algorithms were implemented to extract the optimal patterns from a given dictionary. They carried out a new insight on the sparse representations. In this communication, this way is followed. It takes into account the goal to obtain a sparse multiscale decomposition with the different constraints: i/ to get a sparse representation with patterns looking like to Gaussian functions, ii/ to be able to decompose into patterns with only positive amplitudes, iii/ to get a representation from a translated and dilated pattern, iv/ to constrain the representation by a threshold, v/ to separate the sparse signal from a smooth baseline. Different greedy algorithms were built from the use of redundant wavelet transforms (pyramidal and `a trous ones), for 1D signals and 2D images. Experimentations on astronomical images allow one a gain of about two in sparsity compared to a classical DWT thresholding. A fine denoising is obtained. The results do not display any wavy artifacts. This decomposition is an efficient tool for astronomical image analysis
- …