1,772 research outputs found
Spatially adaptive estimation via fitted local likelihood techniques
This paper offers a new technique for spatially adaptive estimation. The local likelihood is exploited for nonparametric modelling of observations and estimated signals. The approach is based on the assumption of a local homogeneity of the signal: for every point there exists a neighborhood in which the signal can be well approximated by a constant. The fitted local likelihood statistics is used for selection of an adaptive size of this neighborhood. The algorithm is developed for quite a general class of observations subject to the exponential distribution. The estimated signal can be uni- and multivariable. We demonstrate a good performance of the new algorithm for Poissonian image denoising and compare of the new method versus the intersection of confidence interval technique that also exploits a selection of an adaptive neighborhood for estimation
WARP: Wavelets with adaptive recursive partitioning for multi-dimensional data
Effective identification of asymmetric and local features in images and other
data observed on multi-dimensional grids plays a critical role in a wide range
of applications including biomedical and natural image processing. Moreover,
the ever increasing amount of image data, in terms of both the resolution per
image and the number of images processed per application, requires algorithms
and methods for such applications to be computationally efficient. We develop a
new probabilistic framework for multi-dimensional data to overcome these
challenges through incorporating data adaptivity into discrete wavelet
transforms, thereby allowing them to adapt to the geometric structure of the
data while maintaining the linear computational scalability. By exploiting a
connection between the local directionality of wavelet transforms and recursive
dyadic partitioning on the grid points of the observation, we obtain the
desired adaptivity through adding to the traditional Bayesian wavelet
regression framework an additional layer of Bayesian modeling on the space of
recursive partitions over the grid points. We derive the corresponding
inference recipe in the form of a recursive representation of the exact
posterior, and develop a class of efficient recursive message passing
algorithms for achieving exact Bayesian inference with a computational
complexity linear in the resolution and sample size of the images. While our
framework is applicable to a range of problems including multi-dimensional
signal processing, compression, and structural learning, we illustrate its work
and evaluate its performance in the context of 2D and 3D image reconstruction
using real images from the ImageNet database. We also apply the framework to
analyze a data set from retinal optical coherence tomography
Structural adaptive smoothing: Principles and applications in imaging
Structural adaptive smoothing provides a new concept of edge-preserving non-parametric smoothing methods. In imaging it employs qualitative assumption on the underlying homogeneity structure of the image. The chapter describes the main principles of the approach and discusses applications ranging from image denoising to the analysis of functional and diffusion weighted Magnetic Resonance experiments
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Spatially adaptive estimation via fitted local likelihood techniques
This paper offers a new technique for spatially adaptive estimation.
The local likelihood is exploited for nonparametric modelling of observations
and estimated signals. The approach is based on the assumption of a local
homogeneity of the signal: for every point there exists a neighborhood in
which the signal can be well approximated by a constant. The fitted local
likelihood statistics is used for selection of an adaptive size of this
neighborhood. The algorithm is developed for quite a general class of
observations subject to the exponential distribution. The estimated signal
can be uni- and multivariable. We demonstrate a good performance of the new
algorithm for Poissonian image denoising and compare of the new method versus
the intersection of confidence interval technique that also exploits
a selection of an adaptive neighborhood for estimation
Total variation versus waveletâbased methods for image denoising in fluorescence lifetime imaging microscopy
We report the first application of waveletâbased denoising (noise removal) methods to timeâdomain boxâcar fluorescence lifetime imaging microscopy (FLIM) images and compare the results to novel total variation (TV) denoising methods. Methods were tested first on artificial images and then applied to lowâlight liveâcell images. Relative to undenoised images, TV methods could improve lifetime precision up to 10âfold in artificial images, while preserving the overall accuracy of lifetime and amplitude values of a singleâexponential decay model and improving local lifetime fitting in liveâcell images. Waveletâbased methods were at least 4âfold faster than TV methods, but could introduce significant inaccuracies in recovered lifetime values. The denoising methods discussed can potentially enhance a variety of FLIM applications, including liveâcell, in vivo animal, or endoscopic imaging studies, especially under challenging imaging conditions such as lowâlight or fast videoârate imaging. (© 2012 WILEYâVCH Verlag GmbH & Co. KGaA, Weinheim)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91192/1/449_ftp.pd
The Propagation-Separation Approach
Lokal parametrische Modelle werden hĂ€ufig im Kontext der nichtparametrischen SchĂ€tzung verwendet. Bei einer punktweisen SchĂ€tzung der Zielfunktion können die parametrischen Umgebungen mithilfe von Gewichten beschrieben werden, die entweder von den Designpunkten oder (zusĂ€tzlich) von den Beobachtungen abhĂ€ngen. Der Vergleich von verrauschten Beobachtungen in einzelnen Punkten leidet allerdings unter einem Mangel an Robustheit. Der Propagations-Separations-Ansatz von Polzehl und Spokoiny [2006] verwendet daher einen Multiskalen-Ansatz mit iterativ aktualisierten Gewichten. Wir prĂ€sentieren hier eine theoretische Studie und numerische Resultate, die ein besseres VerstĂ€ndnis des Verfahrens ermöglichen. Zu diesem Zweck definieren und untersuchen wir eine neue Strategie fĂŒr die Wahl des entscheidenden Parameters des Verfahrens, der Adaptationsbandweite. Insbesondere untersuchen wir ihre VariabilitĂ€t in AbhĂ€ngigkeit von der unbekannten Zielfunktion. Unsere Resultate rechtfertigen eine Wahl, die unabhĂ€ngig von den jeweils vorliegenden Beobachtungen ist. Die neue Parameterwahl liefert fĂŒr stĂŒckweise konstante und stĂŒckweise beschrĂ€nkte Funktionen theoretische Beweise der Haupteigenschaften des Algorithmus. FĂŒr den Fall eines falsch spezifizierten Modells fĂŒhren wir eine spezielle Stufenfunktion ein und weisen eine punktweise Fehlerschranke im Vergleich zum SchĂ€tzer des Algorithmus nach. Des Weiteren entwickeln wir eine neue Methode zur Entrauschung von diffusionsgewichteten Magnetresonanzdaten. Unser neues Verfahren (ms)POAS basiert auf einer speziellen Beschreibung der Daten, die eine zeitgleiche GlĂ€ttung bezĂŒglich der gemessenen Positionen und der Richtungen der verwendeten Diffusionsgradienten ermöglicht. FĂŒr den kombinierten Messraum schlagen wir zwei Distanzfunktionen vor, deren Eignung wir mithilfe eines differentialgeometrischen Ansatzes nachweisen. SchlieĂlich demonstrieren wir das groĂe Potential von (ms)POAS auf simulierten und experimentellen Daten.In statistics, nonparametric estimation is often based on local parametric modeling. For pointwise estimation of the target function, the parametric neighborhoods can be described by weights that depend on design points or on observations. As it turned out, the comparison of noisy observations at single points suffers from a lack of robustness. The Propagation-Separation Approach by Polzehl and Spokoiny [2006] overcomes this problem by using a multiscale approach with iteratively updated weights. The method has been successfully applied to a large variety of statistical problems. Here, we present a theoretical study and numerical results, which provide a better understanding of this versatile procedure. For this purpose, we introduce and analyse a novel strategy for the choice of the crucial parameter of the algorithm, namely the adaptation bandwidth. In particular, we study its variability with respect to the unknown target function. This justifies a choice independent of the data at hand. For piecewise constant and piecewise bounded functions, this choice enables theoretical proofs of the main heuristic properties of the algorithm. Additionally, we consider the case of a misspecified model. Here, we introduce a specific step function, and we establish a pointwise error bound between this function and the corresponding estimates of the Propagation-Separation Approach. Finally, we develop a method for the denoising of diffusion-weighted magnetic resonance data, which is based on the Propagation-Separation Approach. Our new procedure, called (ms)POAS, relies on a specific description of the data, which enables simultaneous smoothing in the measured positions and with respect to the directions of the applied diffusion-weighting magnetic field gradients. We define and justify two distance functions on the combined measurement space, where we follow a differential geometric approach. We demonstrate the capability of (ms)POAS on simulated and experimental data
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