Weyl-Heisenberg Spaces for Robust Orthogonal Frequency Division Multiplexing

Design of Weyl-Heisenberg sets of waveforms for robust orthogonal frequency division multiplex- ing (OFDM) has been the subject of a considerable volume of work. In this paper, a complete parameterization of orthogonal Weyl-Heisenberg sets and their corresponding biorthogonal sets is given. Several examples of Weyl-Heisenberg sets designed using this parameterization are pre- sented, which in simulations show a high potential for enabling OFDM robust to frequency offset, timing mismatch, and narrow-band interference

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

Wavelet treatment of the intra-chain correlation functions of homopolymers in dilute solutions

Discrete wavelets are applied to parametrization of the intra-chain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulation. Several orthogonal and biorthogonal basis sets have been investigated for use in the truncated wavelet approximation. Quality of the approximation has been assessed by calculation of the scaling exponents obtained from des Cloizeaux ansatz for the correlation functions of homopolymers with different connectivities in a good solvent. The resulting exponents are in a better agreement with those from the recent renormalisation group calculations as compared to the data without the wavelet denoising. We also discuss how the wavelet treatment improves the quality of data for correlation functions from simulations of homopolymers at varied solvent conditions and of heteropolymers.Comment: RevTeX, 19 pages, 7 PS figures. Accepted for publication in PR

Algorithms and Architectures for Secure Embedded Multimedia Systems

Embedded multimedia systems provide real-time video support for applications in entertainment (mobile phones, internet video websites), defense (video-surveillance and tracking) and public-domain (tele-medicine, remote and distant learning, traffic monitoring and management). With the widespread deployment of such real-time embedded systems, there has been an increasing concern over the security and authentication of concerned multimedia data. While several (software) algorithms and hardware architectures have been proposed in the research literature to support multimedia security, these fail to address embedded applications whose performance specifications have tighter constraints on computational power and available hardware resources. The goals of this dissertation research are two fold: 1. To develop novel algorithms for joint video compression and encryption. The proposed algorithms reduce the computational requirements of multimedia encryption algorithms. We propose an approach that uses the compression parameters instead of compressed bitstream for video encryption. 2. Hardware acceleration of proposed algorithms over reconfigurable computing platforms such as FPGA and over VLSI circuits. We use signal processing knowledge to make the algorithms suitable for hardware optimizations and try to reduce the critical path of circuits using hardware-specific optimizations. The proposed algorithms ensures a considerable level of security for low-power embedded systems such as portable video players and surveillance cameras. These schemes have zero or little compression losses and preserve the desired properties of compressed bitstream in encrypted bitstream to ensure secure and scalable transmission of videos over heterogeneous networks. They also support indexing, search and retrieval in secure multimedia digital libraries. This property is crucial not only for police and armed forces to retrieve information about a suspect from a large video database of surveillance feeds, but extremely helpful for data centers (such as those used by youtube, aol and metacafe) in reducing the computation cost in search and retrieval of desired videos

First-arrival Travel-Time Tomography using Second Generation Wavelets

International audienceWavelet decomposition of the slowness model has been proposed as a multiscale strategy for seismic first-arrival time tomography. We propose the introduction of so-called second generation wavelets which could be used for any mesh structure and does not need a number of samples as the power of two in each direction. Moreover, one can handle easily boundary effects. A linearized procedure for inverting delayed travel-times considering either slowness coefficients or wavelet coefficients. The ray tracing is solved at each iteration through an eikonal solver while the linear system to be solved at each iteration goes through an iterative solver as LSQR algorithm. We develop wavelet decomposition over constant patches (Haar wavelet) or over linear patches (Battle-Lemarie wavelet) of coefficients at different scales. This decomposition is introduced in the linear system to be solved and wavelet coefficients are considered as unknowns to be inverted. Synthetic examples show that the inversion behaves in a better way as wavelet decomposition seems to act as a preconditioner of the linear system. Local discretisation is possible but requires additional implementation as artefacs once built inside the model description never disappear because of the linearized approach. A binary mask operator is designed for each scale grid and could be applied locally leading to quite different spatial resolution depending on the analysis we could perform of the expected resolution at a given position of the medium. We show that indeed it is possible to design this binary operator and we apply it to synthetic examples as a crosswell experiment inside the Marmousi model. An application to a surface-surface experiment has been performed and the waveled decomposition shows that indeed we may recover detailed features nearby the free surface while preventing imprints of ray coverage at greater depths giving us smooth features at that depths. In spite of the increase demand of computer resources, the wavelet decomposition seems to be a rather promising alternative for controlling the resolution variation of seismic first-arrival tomography

Stochastic filtering via L2 projection on mixture manifolds with computer algorithms and numerical examples

We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric and on a family of normal mixtures. We compare this method to earlier projection methods based on the Hellinger distance/Fisher metric and exponential families, and we compare the L2 mixture projection filter with a particle method with the same number of parameters, using the Levy metric. We prove that for a simple choice of the mixture manifold the L2 mixture projection filter coincides with a Galerkin method, whereas for more general mixture manifolds the equivalence does not hold and the L2 mixture filter is more general. We study particular systems that may illustrate the advantages of this new filter over other algorithms when comparing outputs with the optimal filter. We finally consider a specific software design that is suited for a numerically efficient implementation of this filter and provide numerical examples.Comment: Updated and expanded version published in the Journal reference below. Preprint updates: January 2016 (v3) added projection of Zakai Equation and difference with projection of Kushner-Stratonovich (section 4.1). August 2014 (v2) added Galerkin equivalence proof (Section 5) to the March 2013 (v1) versio