7,201 research outputs found
Left-invariant evolutions of wavelet transforms on the Similitude Group
Enhancement of multiple-scale elongated structures in noisy image data is
relevant for many biomedical applications but commonly used PDE-based
enhancement techniques often fail at crossings in an image. To get an overview
of how an image is composed of local multiple-scale elongated structures we
construct a multiple scale orientation score, which is a continuous wavelet
transform on the similitude group, SIM(2). Our unitary transform maps the space
of images onto a reproducing kernel space defined on SIM(2), allowing us to
robustly relate Euclidean (and scaling) invariant operators on images to
left-invariant operators on the corresponding continuous wavelet transform.
Rather than often used wavelet (soft-)thresholding techniques, we employ the
group structure in the wavelet domain to arrive at left-invariant evolutions
and flows (diffusion), for contextual crossing preserving enhancement of
multiple scale elongated structures in noisy images. We present experiments
that display benefits of our work compared to recent PDE techniques acting
directly on the images and to our previous work on left-invariant diffusions on
orientation scores defined on Euclidean motion group.Comment: 40 page
Empirical Bayes selection of wavelet thresholds
This paper explores a class of empirical Bayes methods for level-dependent
threshold selection in wavelet shrinkage. The prior considered for each wavelet
coefficient is a mixture of an atom of probability at zero and a heavy-tailed
density. The mixing weight, or sparsity parameter, for each level of the
transform is chosen by marginal maximum likelihood. If estimation is carried
out using the posterior median, this is a random thresholding procedure; the
estimation can also be carried out using other thresholding rules with the same
threshold. Details of the calculations needed for implementing the procedure
are included. In practice, the estimates are quick to compute and there is
software available. Simulations on the standard model functions show excellent
performance, and applications to data drawn from various fields of application
are used to explore the practical performance of the approach. By using a
general result on the risk of the corresponding marginal maximum likelihood
approach for a single sequence, overall bounds on the risk of the method are
found subject to membership of the unknown function in one of a wide range of
Besov classes, covering also the case of f of bounded variation. The rates
obtained are optimal for any value of the parameter p in (0,\infty],
simultaneously for a wide range of loss functions, each dominating the L_q norm
of the \sigmath derivative, with \sigma\ge0 and 0<q\le2.Comment: Published at http://dx.doi.org/10.1214/009053605000000345 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Non-parametric linear time-invariant system identification by discrete wavelet transforms
We describe the use of the discrete wavelet transform (DWT) for non-parametric linear time-invariant system identification. Identification is achieved by using a test excitation to the system under test (SUT) that also acts as the analyzing function for the DWT of the SUT's output, so as to recover the impulse response. The method uses as excitation any signal that gives an orthogonal inner product in the DWT at some step size (that cannot be 1). We favor wavelet scaling coefficients as excitations, with a step size of 2. However, the system impulse or frequency response can then only be estimated at half the available number of points of the sampled output sequence, introducing a multirate problem that means we have to 'oversample' the SUT output. The method has several advantages over existing techniques, e.g., it uses a simple, easy to generate excitation, and avoids the singularity problems and the (unbounded) accumulation of round-off errors that can occur with standard techniques. In extensive simulations, identification of a variety of finite and infinite impulse response systems is shown to be considerably better than with conventional system identification methods.Department of Computin
Fingerprint Recognition Using Translation Invariant Scattering Network
Fingerprint recognition has drawn a lot of attention during last decades.
Different features and algorithms have been used for fingerprint recognition in
the past. In this paper, a powerful image representation called scattering
transform/network, is used for recognition. Scattering network is a
convolutional network where its architecture and filters are predefined wavelet
transforms. The first layer of scattering representation is similar to sift
descriptors and the higher layers capture higher frequency content of the
signal. After extraction of scattering features, their dimensionality is
reduced by applying principal component analysis (PCA). At the end, multi-class
SVM is used to perform template matching for the recognition task. The proposed
scheme is tested on a well-known fingerprint database and has shown promising
results with the best accuracy rate of 98\%.Comment: IEEE Signal Processing in Medicine and Biology Symposium, 201
The WaveD Transform in R: Performs Fast Translation-Invariant Wavelet Deconvolution
This paper provides an introduction to a software package called waved making available all code necessary for reproducing the figures in the recently published articles on the WaveD transform for wavelet deconvolution of noisy signals. The forward WaveD transforms and their inverses can be computed using any wavelet from the Meyer family. The WaveD coefficients can be depicted according to time and resolution in several ways for data analysis. The algorithm which implements the translation invariant WaveD transform takes full advantage of the fast Fourier transform (FFT) and runs in O(n(log n)^2)steps only. The waved package includes functions to perform thresholding and tne resolution tuning according to methods in the literature as well as newly designed visual and statistical tools for assessing WaveD fits. We give a waved tutorial session and review benchmark examples of noisy convolutions to illustrate the non-linear adaptive properties of wavelet deconvolution.
A Comparative study of Arabic handwritten characters invariant feature
This paper is practically interested in the unchangeable feature of Arabic
handwritten character. It presents results of comparative study achieved on
certain features extraction techniques of handwritten character, based on Hough
transform, Fourier transform, Wavelet transform and Gabor Filter. Obtained
results show that Hough Transform and Gabor filter are insensible to the
rotation and translation, Fourier Transform is sensible to the rotation but
insensible to the translation, in contrast to Hough Transform and Gabor filter,
Wavelets Transform is sensitive to the rotation as well as to the translation
On The Continuous Steering of the Scale of Tight Wavelet Frames
In analogy with steerable wavelets, we present a general construction of
adaptable tight wavelet frames, with an emphasis on scaling operations. In
particular, the derived wavelets can be "dilated" by a procedure comparable to
the operation of steering steerable wavelets. The fundamental aspects of the
construction are the same: an admissible collection of Fourier multipliers is
used to extend a tight wavelet frame, and the "scale" of the wavelets is
adapted by scaling the multipliers. As an application, the proposed wavelets
can be used to improve the frequency localization. Importantly, the localized
frequency bands specified by this construction can be scaled efficiently using
matrix multiplication
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