253 research outputs found
Audio Source Separation Using Sparse Representations
This is the author's final version of the article, first published as A. Nesbit, M. G. Jafari, E. Vincent and M. D. Plumbley. Audio Source Separation Using Sparse Representations. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 10, pp. 246-264. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch010file: NesbitJafariVincentP11-audio.pdf:n\NesbitJafariVincentP11-audio.pdf:PDF owner: markp timestamp: 2011.02.04file: NesbitJafariVincentP11-audio.pdf:n\NesbitJafariVincentP11-audio.pdf:PDF owner: markp timestamp: 2011.02.04The authors address the problem of audio source separation, namely, the recovery of audio signals from recordings of mixtures of those signals. The sparse component analysis framework is a powerful method for achieving this. Sparse orthogonal transforms, in which only few transform coefficients differ significantly from zero, are developed; once the signal has been transformed, energy is apportioned from each transform coefficient to each estimated source, and, finally, the signal is reconstructed using the inverse transform. The overriding aim of this chapter is to demonstrate how this framework, as exemplified here by two different decomposition methods which adapt to the signal to represent it sparsely, can be used to solve different problems in different mixing scenarios. To address the instantaneous (neither delays nor echoes) and underdetermined (more sources than mixtures) mixing model, a lapped orthogonal transform is adapted to the signal by selecting a basis from a library of predetermined bases. This method is highly related to the windowing methods used in the MPEG audio coding framework. In considering the anechoic (delays but no echoes) and determined (equal number of sources and mixtures) mixing case, a greedy adaptive transform is used based on orthogonal basis functions that are learned from the observed data, instead of being selected from a predetermined library of bases. This is found to encode the signal characteristics, by introducing a feedback system between the bases and the observed data. Experiments on mixtures of speech and music signals demonstrate that these methods give good signal approximations and separation performance, and indicate promising directions for future research
Multi-resolution two-sample comparison through the divide-merge Markov tree
We introduce a probabilistic framework for two-sample comparison based on a
nonparametric process taking the form of a Markov model that transitions
between a "divide" and a "merge" state on a multi-resolution partition tree of
the sample space. Multi-scale two-sample comparison is achieved through
inferring the underlying state of the process along the partition tree. The
Markov design allows the process to incorporate spatial clustering of
differential structures, which is commonly observed in two-sample problems but
ignored by existing methods. Inference is carried out under the Bayesian
paradigm through recursive propagation algorithms. We demonstrate the work of
our method through simulated data and a real flow cytometry data set, and show
that it substantially outperforms other state-of-the-art two-sample tests in
several settings.Comment: Corrected typos. Added Software sectio
Quadtree Structured Approximation Algorithms
The success of many image restoration algorithms is often due to their ability to sparsely describe the original signal. Many sparse promoting transforms exist, including wavelets, the so called ‘lets’ family of transforms and more recent non-local learned transforms. The first part of this thesis reviews sparse approximation theory, particularly in relation to 2-D piecewise polynomial signals. We also show the connection between this theory and current state of the art algorithms that cover the following image restoration and enhancement applications: denoising, deconvolution, interpolation and multi-view super resolution.
In [63], Shukla et al. proposed a compression algorithm, based on a sparse quadtree decomposition model, which could optimally represent piecewise polynomial images. In the second part of this thesis we adapt this model to image restoration by changing the rate-distortion penalty to a description-length penalty. Moreover, one of the major drawbacks of this type of approximation is the computational complexity required to find a suitable subspace for each node of the quadtree. We address this issue by searching for a suitable subspace much more efficiently using the mathematics of updating matrix factorisations. Novel algorithms are developed to tackle the four problems previously mentioned. Simulation results indicate that we beat state of the art results when the original signal is in the model (e.g. depth images) and are competitive for natural images when the degradation is high.Open Acces
Sparse representation based hyperspectral image compression and classification
Abstract
This thesis presents a research work on applying sparse representation to lossy hyperspectral image
compression and hyperspectral image classification. The proposed lossy hyperspectral image
compression framework introduces two types of dictionaries distinguished by the terms sparse
representation spectral dictionary (SRSD) and multi-scale spectral dictionary (MSSD), respectively.
The former is learnt in the spectral domain to exploit the spectral correlations, and the
latter in wavelet multi-scale spectral domain to exploit both spatial and spectral correlations in
hyperspectral images. To alleviate the computational demand of dictionary learning, either a
base dictionary trained offline or an update of the base dictionary is employed in the compression
framework. The proposed compression method is evaluated in terms of different objective
metrics, and compared to selected state-of-the-art hyperspectral image compression schemes, including
JPEG 2000. The numerical results demonstrate the effectiveness and competitiveness of
both SRSD and MSSD approaches.
For the proposed hyperspectral image classification method, we utilize the sparse coefficients
for training support vector machine (SVM) and k-nearest neighbour (kNN) classifiers. In particular,
the discriminative character of the sparse coefficients is enhanced by incorporating contextual
information using local mean filters. The classification performance is evaluated and compared
to a number of similar or representative methods. The results show that our approach could outperform
other approaches based on SVM or sparse representation.
This thesis makes the following contributions. It provides a relatively thorough investigation
of applying sparse representation to lossy hyperspectral image compression. Specifically,
it reveals the effectiveness of sparse representation for the exploitation of spectral correlations
in hyperspectral images. In addition, we have shown that the discriminative character of sparse
coefficients can lead to superior performance in hyperspectral image classification.EM201
Poisson noise reduction with non-local PCA
Photon-limited imaging arises when the number of photons collected by a
sensor array is small relative to the number of detector elements. Photon
limitations are an important concern for many applications such as spectral
imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson
distribution is used to model these observations, and the inherent
heteroscedasticity of the data combined with standard noise removal methods
yields significant artifacts. This paper introduces a novel denoising algorithm
for photon-limited images which combines elements of dictionary learning and
sparse patch-based representations of images. The method employs both an
adaptation of Principal Component Analysis (PCA) for Poisson noise and recently
developed sparsity-regularized convex optimization algorithms for
photon-limited images. A comprehensive empirical evaluation of the proposed
method helps characterize the performance of this approach relative to other
state-of-the-art denoising methods. The results reveal that, despite its
conceptual simplicity, Poisson PCA-based denoising appears to be highly
competitive in very low light regimes.Comment: erratum: Image man is wrongly name pepper in the journal versio
- …