1,076 research outputs found
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Multichannel high resolution NMF for modelling convolutive mixtures of non-stationary signals in the time-frequency domain
Several probabilistic models involving latent components have been proposed for modeling time-frequency (TF) representations of audio signals such as spectrograms, notably in the nonnegative matrix factorization (NMF) literature. Among them, the recent high-resolution NMF (HR-NMF) model is able to take both phases and local correlations in each frequency band into account, and its potential has been illustrated in applications such as source separation and audio inpainting. In this paper, HR-NMF is extended to multichannel signals and to convolutive mixtures. The new model can represent a variety of stationary and non-stationary signals, including autoregressive moving average (ARMA) processes and mixtures of damped sinusoids. A fast variational expectation-maximization (EM) algorithm is proposed to estimate the enhanced model. This algorithm is applied to piano signals, and proves capable of accurately modeling reverberation, restoring missing observations, and separating pure tones with close frequencies
DPO - Denoising, Deconvolving, and Decomposing Photon Observations
The analysis of astronomical images is a non-trivial task. The D3PO algorithm
addresses the inference problem of denoising, deconvolving, and decomposing
photon observations. Its primary goal is the simultaneous but individual
reconstruction of the diffuse and point-like photon flux given a single photon
count image, where the fluxes are superimposed. In order to discriminate
between these morphologically different signal components, a probabilistic
algorithm is derived in the language of information field theory based on a
hierarchical Bayesian parameter model. The signal inference exploits prior
information on the spatial correlation structure of the diffuse component and
the brightness distribution of the spatially uncorrelated point-like sources. A
maximum a posteriori solution and a solution minimizing the Gibbs free energy
of the inference problem using variational Bayesian methods are discussed.
Since the derivation of the solution is not dependent on the underlying
position space, the implementation of the D3PO algorithm uses the NIFTY package
to ensure applicability to various spatial grids and at any resolution. The
fidelity of the algorithm is validated by the analysis of simulated data,
including a realistic high energy photon count image showing a 32 x 32 arcmin^2
observation with a spatial resolution of 0.1 arcmin. In all tests the D3PO
algorithm successfully denoised, deconvolved, and decomposed the data into a
diffuse and a point-like signal estimate for the respective photon flux
components.Comment: 22 pages, 8 figures, 2 tables, accepted by Astronomy & Astrophysics;
refereed version, 1 figure added, results unchanged, software available at
http://www.mpa-garching.mpg.de/ift/d3po
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