35,334 research outputs found
Blind deconvolution of medical ultrasound images: parametric inverse filtering approach
©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.910179The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a ldquohybridizationrdquo of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the ldquohybridrdquo approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolution algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used
Stochastic Wiener Filter in the White Noise Space
In this paper we introduce a new approach to the study of filtering theory by
allowing the system's parameters to have a random character. We use Hida's
white noise space theory to give an alternative characterization and a proper
generalization to the Wiener filter over a suitable space of stochastic
distributions introduced by Kondratiev. The main idea throughout this paper is
to use the nuclearity of this spaces in order to view the random variables as
bounded multiplication operators (with respect to the Wick product) between
Hilbert spaces of stochastic distributions. This allows us to use operator
theory tools and properties of Wiener algebras over Banach spaces to proceed
and characterize the Wiener filter equations under the underlying randomness
assumptions
Nonlinear denoising of transient signals with application to event related potentials
We present a new wavelet based method for the denoising of {\it event related
potentials} ERPs), employing techniques recently developed for the paradigm of
deterministic chaotic systems. The denoising scheme has been constructed to be
appropriate for short and transient time sequences using circular state space
embedding. Its effectiveness was successfully tested on simulated signals as
well as on ERPs recorded from within a human brain. The method enables the
study of individual ERPs against strong ongoing brain electrical activity.Comment: 16 pages, Postscript, 6 figures, Physica D in pres
On the relationships between Fourier - Stieltjes coefficients and spectra of measures
We construct examples of uncountable compact subsets of complex numbers with
the property that any Borel measure on the circle group taking values of its
Fourier coefficients from this set has natural spectrum. For measures with
Fourier coefficients tending to 0 we construct tho open set with this property.Comment: 28 page
Multidimensional sampling for simulation and integration: measures, discrepancies, and quasi-random numbers
This is basically a review of the field of Quasi-Monte Carlo intended for
computational physicists and other potential users of quasi-random numbers. As
such, much of the material is not new, but is presented here in a style
hopefully more accessible to physicists than the specialized mathematical
literature. There are also some new results: On the practical side we give
important empirical properties of large quasi-random point sets, especially the
exact quadratic discrepancies; on the theoretical side, there is the exact
distribution of quadratic discrepancy for random point sets.Comment: 51 pages. Full paper, including all figures also available at:
ftp://ftp.nikhef.nl/pub/preprints/96-017.ps.gz Accepted for publication in
Comp.Phys.Comm. Fixed some typos, corrected formula 108,figure 11 and table
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