41 research outputs found
Delay-Coordinates Embeddings as a Data Mining Tool for Denoising Speech Signals
In this paper we utilize techniques from the theory of non-linear dynamical
systems to define a notion of embedding threshold estimators. More specifically
we use delay-coordinates embeddings of sets of coefficients of the measured
signal (in some chosen frame) as a data mining tool to separate structures that
are likely to be generated by signals belonging to some predetermined data set.
We describe a particular variation of the embedding threshold estimator
implemented in a windowed Fourier frame, and we apply it to speech signals
heavily corrupted with the addition of several types of white noise. Our
experimental work seems to suggest that, after training on the data sets of
interest,these estimators perform well for a variety of white noise processes
and noise intensity levels. The method is compared, for the case of Gaussian
white noise, to a block thresholding estimator
Entropy Encoding, Hilbert Space and Karhunen-Loeve Transforms
By introducing Hilbert space and operators, we show how probabilities,
approximations and entropy encoding from signal and image processing allow
precise formulas and quantitative estimates. Our main results yield orthogonal
bases which optimize distinct measures of data encoding.Comment: 25 pages, 1 figur
Local Inversion of the Radon Transform in Even Dimensions Using Wavelets
We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform. These formulas are almost local for even dimensions in the sense that for a given mean square error we can decide which lines near a point must be used to approximate the function at the point within the given error
Wavelet-based Multiresolution Local Tomography
We develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross section of a body, using almost completely local data which significantly reduces the amount of exposure and computations in X-ray tomography. This property which distinguishes our algorithm from the previous algorithms is based on the observation that for some wavelet basis with sufficiently many vanishing moments, the ramp-filtered version of the scaling function as well as the wavelet function has extremely rapid decay. We show that the variance of the elements of the null-space is negligible in the locally reconstructed image. Also we find an upper bound for the reconstruction error in terms of the amount of data used in the algorithm. To reconstruct a local region 20 pixels in radius in a 256 \Theta 256 image we require 12:5% of full e..