5,864 research outputs found
Adaptive lifting schemes with perfect reconstruction
In this paper, we propose a framework for constructing adaptive wavelet decompositions using the lifting scheme. A major requirement is that perfect reconstruction is possible without any overhead cost. In this paper we restrict ourselves to the update lifting stage. It is assumed that the update filter utilises local gradient information to adapt itself to the signal in the sense that smaller gradients `evoke' stronger update filters. As a result, sharp transitions in a signal will not be smoothed to the same extent as regions which are more homogeneous. The approach taken in this paper differs from other adaptive schemes found in the literature in the sense that that no bookkeeping is required in order to have perfect reconstruction
Non-equispaced B-spline wavelets
This paper has three main contributions. The first is the construction of
wavelet transforms from B-spline scaling functions defined on a grid of
non-equispaced knots. The new construction extends the equispaced,
biorthogonal, compactly supported Cohen-Daubechies-Feauveau wavelets. The new
construction is based on the factorisation of wavelet transforms into lifting
steps. The second and third contributions are new insights on how to use these
and other wavelets in statistical applications. The second contribution is
related to the bias of a wavelet representation. It is investigated how the
fine scaling coefficients should be derived from the observations. In the
context of equispaced data, it is common practice to simply take the
observations as fine scale coefficients. It is argued in this paper that this
is not acceptable for non-interpolating wavelets on non-equidistant data.
Finally, the third contribution is the study of the variance in a
non-orthogonal wavelet transform in a new framework, replacing the numerical
condition as a measure for non-orthogonality. By controlling the variances of
the reconstruction from the wavelet coefficients, the new framework allows us
to design wavelet transforms on irregular point sets with a focus on their use
for smoothing or other applications in statistics.Comment: 42 pages, 2 figure
Audio Coding Based on Integer Transforms
Die Audiocodierung hat sich in den letzten Jahren zu einem sehr
populären Forschungs- und Anwendungsgebiet entwickelt. Insbesondere
gehörangepasste Verfahren zur Audiocodierung, wie etwa MPEG-1 Layer-3
(MP3) oder MPEG-2 Advanced Audio Coding (AAC), werden häufig zur
effizienten Speicherung und Ăśbertragung von Audiosignalen verwendet. FĂĽr
professionelle Anwendungen, wie etwa die Archivierung und Ăśbertragung im
Studiobereich, ist hingegen eher eine verlustlose Audiocodierung angebracht.
Die bisherigen Ansätze für gehörangepasste und verlustlose
Audiocodierung sind technisch völlig verschieden. Moderne
gehörangepasste Audiocoder basieren meist auf Filterbänken, wie etwa der
ĂĽberlappenden orthogonalen Transformation "Modifizierte Diskrete
Cosinus-Transformation" (MDCT). Verlustlose Audiocoder hingegen
verwenden meist prädiktive Codierung zur Redundanzreduktion. Nur wenige
Ansätze zur transformationsbasierten verlustlosen Audiocodierung wurden
bisher versucht.
Diese Arbeit präsentiert einen neuen Ansatz hierzu, der das
Lifting-Schema auf die in der gehörangepassten Audiocodierung
verwendeten überlappenden Transformationen anwendet. Dies ermöglicht
eine invertierbare Integer-Approximation der ursprĂĽnglichen
Transformation, z.B. die IntMDCT als Integer-Approximation der MDCT. Die
selbe Technik kann auch für Filterbänke mit niedriger Systemverzögerung
angewandt werden. Weiterhin ermöglichen ein neuer, mehrdimensionaler
Lifting-Ansatz und eine Technik zur Spektralformung von
Quantisierungsfehlern eine Verbesserung der Approximation der
ursprĂĽnglichen Transformation.
Basierend auf diesen neuen Integer-Transformationen werden in dieser
Arbeit neue Verfahren zur Audiocodierung vorgestellt. Die Verfahren
umfassen verlustlose Audiocodierung, eine skalierbare verlustlose
Erweiterung eines gehörangepassten Audiocoders und einen integrierten
Ansatz zur fein skalierbaren gehörangepassten und verlustlosen
Audiocodierung. SchlieĂźlich wird mit Hilfe der Integer-Transformationen
ein neuer Ansatz zur unhörbaren Einbettung von Daten mit hohen
Datenraten in unkomprimierte Audiosignale vorgestellt.In recent years audio coding has become a very popular field for
research and applications. Especially perceptual audio coding schemes,
such as MPEG-1 Layer-3 (MP3) and MPEG-2 Advanced Audio Coding (AAC), are
widely used for efficient storage and transmission of music
signals. Nevertheless, for professional applications, such as archiving
and transmission in studio environments, lossless audio coding schemes
are considered more appropriate.
Traditionally, the technical approaches used in perceptual and lossless
audio coding have been separate worlds. In perceptual audio coding, the
use of filter banks, such as the lapped orthogonal transform "Modified
Discrete Cosine Transform" (MDCT), has been the approach of choice being
used by many state of the art coding schemes. On the other hand,
lossless audio coding schemes mostly employ predictive coding of
waveforms to remove redundancy. Only few attempts have been made so far
to use transform coding for the purpose of lossless audio coding.
This work presents a new approach of applying the lifting scheme to
lapped transforms used in perceptual audio coding. This allows for an
invertible integer-to-integer approximation of the original transform,
e.g. the IntMDCT as an integer approximation of the MDCT. The same
technique can also be applied to low-delay filter banks. A generalized,
multi-dimensional lifting approach and a noise-shaping technique are
introduced, allowing to further optimize the accuracy of the
approximation to the original transform.
Based on these new integer transforms, this work presents new audio
coding schemes and applications. The audio coding applications cover
lossless audio coding, scalable lossless enhancement of a perceptual
audio coder and fine-grain scalable perceptual and lossless audio
coding. Finally an approach to data hiding with high data rates in
uncompressed audio signals based on integer transforms is described
Audio Coding Based on Integer Transforms
Die Audiocodierung hat sich in den letzten Jahren zu einem sehr
populären Forschungs- und Anwendungsgebiet entwickelt. Insbesondere
gehörangepasste Verfahren zur Audiocodierung, wie etwa MPEG-1 Layer-3
(MP3) oder MPEG-2 Advanced Audio Coding (AAC), werden häufig zur
effizienten Speicherung und Ăśbertragung von Audiosignalen verwendet. FĂĽr
professionelle Anwendungen, wie etwa die Archivierung und Ăśbertragung im
Studiobereich, ist hingegen eher eine verlustlose Audiocodierung angebracht.
Die bisherigen Ansätze für gehörangepasste und verlustlose
Audiocodierung sind technisch völlig verschieden. Moderne
gehörangepasste Audiocoder basieren meist auf Filterbänken, wie etwa der
ĂĽberlappenden orthogonalen Transformation "Modifizierte Diskrete
Cosinus-Transformation" (MDCT). Verlustlose Audiocoder hingegen
verwenden meist prädiktive Codierung zur Redundanzreduktion. Nur wenige
Ansätze zur transformationsbasierten verlustlosen Audiocodierung wurden
bisher versucht.
Diese Arbeit präsentiert einen neuen Ansatz hierzu, der das
Lifting-Schema auf die in der gehörangepassten Audiocodierung
verwendeten überlappenden Transformationen anwendet. Dies ermöglicht
eine invertierbare Integer-Approximation der ursprĂĽnglichen
Transformation, z.B. die IntMDCT als Integer-Approximation der MDCT. Die
selbe Technik kann auch für Filterbänke mit niedriger Systemverzögerung
angewandt werden. Weiterhin ermöglichen ein neuer, mehrdimensionaler
Lifting-Ansatz und eine Technik zur Spektralformung von
Quantisierungsfehlern eine Verbesserung der Approximation der
ursprĂĽnglichen Transformation.
Basierend auf diesen neuen Integer-Transformationen werden in dieser
Arbeit neue Verfahren zur Audiocodierung vorgestellt. Die Verfahren
umfassen verlustlose Audiocodierung, eine skalierbare verlustlose
Erweiterung eines gehörangepassten Audiocoders und einen integrierten
Ansatz zur fein skalierbaren gehörangepassten und verlustlosen
Audiocodierung. SchlieĂźlich wird mit Hilfe der Integer-Transformationen
ein neuer Ansatz zur unhörbaren Einbettung von Daten mit hohen
Datenraten in unkomprimierte Audiosignale vorgestellt.In recent years audio coding has become a very popular field for
research and applications. Especially perceptual audio coding schemes,
such as MPEG-1 Layer-3 (MP3) and MPEG-2 Advanced Audio Coding (AAC), are
widely used for efficient storage and transmission of music
signals. Nevertheless, for professional applications, such as archiving
and transmission in studio environments, lossless audio coding schemes
are considered more appropriate.
Traditionally, the technical approaches used in perceptual and lossless
audio coding have been separate worlds. In perceptual audio coding, the
use of filter banks, such as the lapped orthogonal transform "Modified
Discrete Cosine Transform" (MDCT), has been the approach of choice being
used by many state of the art coding schemes. On the other hand,
lossless audio coding schemes mostly employ predictive coding of
waveforms to remove redundancy. Only few attempts have been made so far
to use transform coding for the purpose of lossless audio coding.
This work presents a new approach of applying the lifting scheme to
lapped transforms used in perceptual audio coding. This allows for an
invertible integer-to-integer approximation of the original transform,
e.g. the IntMDCT as an integer approximation of the MDCT. The same
technique can also be applied to low-delay filter banks. A generalized,
multi-dimensional lifting approach and a noise-shaping technique are
introduced, allowing to further optimize the accuracy of the
approximation to the original transform.
Based on these new integer transforms, this work presents new audio
coding schemes and applications. The audio coding applications cover
lossless audio coding, scalable lossless enhancement of a perceptual
audio coder and fine-grain scalable perceptual and lossless audio
coding. Finally an approach to data hiding with high data rates in
uncompressed audio signals based on integer transforms is described
Adaptive polyphase subband decomposition structures for image compression
Cataloged from PDF version of article.Subband decomposition techniques have been extensively used for data coding and analysis. In most filter
banks, the goal is to obtain subsampled signals corresponding to different spectral regions of the original data. However, this approach leads to various artifacts in images having spatially varying characteristics, such as images containing text, subtitles, or sharp edges. In this paper, adaptive filter banks with perfect reconstruction property are presented for such images. The filters of the decomposition structure which can be either linear or nonlinear vary according to the nature of the signal. This leads to improved image compression ratios. Simulation examples are presented
Two-dimensional non separable adaptive lifting scheme for still and stereo image coding
International audienceMany existing works related to lossy-to-lossless image compression are based on the lifting concept. However, it has been observed that the separable lifting scheme structure presents some limitations because of the separable processing performed along the image lines and columns. In this paper, we propose to use a 2D non separable lifting scheme decomposition that enables progressive reconstruction and exact decoding of images. More precisely, we focus on the optimization of all the involved decomposition operators. In this respect, we design the prediction filters by minimizing the variance of the detail signals. Concerning the update filters, we propose a new optimization criterion which aims at reducing the inherent aliasing artefacts. Simulations carried out on still and stereo images show the benefits which can be drawn from the proposed optimization of the lifting operators
Multiresolution signal decomposition schemes. Part 2: Morphological wavelets
In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinear wavelet transforms has been given by the introduction of the lifting scheme by Sweldens. The aim of this report, which is a sequel to a previous report devoted exclusively to the pyramid transform, is to present an axiomatic framework encompassing most existing linear and nonlinear wavelet decompositions. Furthermore, it introduces some, thus far unknown, wavelets based on mathematical morphology, such as the morphological Haar wavelet, both in one and two dimensions. A general and flexible approach for the construction of nonlinear (morphological) wavelets is provided by the lifting scheme. This paper discusses one example in considerable detail, the max-lifting scheme, which has the intriguing property that it preserves local maxima in a signal over a range of scales, depending on how local or global these maxima are
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
The richness of natural images makes the quest for optimal representations in
image processing and computer vision challenging. The latter observation has
not prevented the design of image representations, which trade off between
efficiency and complexity, while achieving accurate rendering of smooth regions
as well as reproducing faithful contours and textures. The most recent ones,
proposed in the past decade, share an hybrid heritage highlighting the
multiscale and oriented nature of edges and patterns in images. This paper
presents a panorama of the aforementioned literature on decompositions in
multiscale, multi-orientation bases or dictionaries. They typically exhibit
redundancy to improve sparsity in the transformed domain and sometimes its
invariance with respect to simple geometric deformations (translation,
rotation). Oriented multiscale dictionaries extend traditional wavelet
processing and may offer rotation invariance. Highly redundant dictionaries
require specific algorithms to simplify the search for an efficient (sparse)
representation. We also discuss the extension of multiscale geometric
decompositions to non-Euclidean domains such as the sphere or arbitrary meshed
surfaces. The etymology of panorama suggests an overview, based on a choice of
partially overlapping "pictures". We hope that this paper will contribute to
the appreciation and apprehension of a stream of current research directions in
image understanding.Comment: 65 pages, 33 figures, 303 reference
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