A Wavelet-Based Algorithm for the Spatial Analysis of Poisson Data

Wavelets are scaleable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero. In addition to their use as source characterizers, wavelet functions are rapidly gaining currency within the source detection field. Wavelet-based source detection involves the correlation of scaled wavelet functions with binned, two-dimensional image data. If the chosen wavelet function exhibits the property of vanishing moments, significantly non-zero correlation coefficients will be observed only where there are high-order variations in the data; e.g., they will be observed in the vicinity of sources. In this paper, we describe the mission-independent, wavelet-based source detection algorithm WAVDETECT, part of the CIAO software package. Aspects of our algorithm include: (1) the computation of local, exposure-corrected normalized (i.e. flat-fielded) background maps; (2) the correction for exposure variations within the field-of-view; (3) its applicability within the low-counts regime, as it does not require a minimum number of background counts per pixel for the accurate computation of source detection thresholds; (4) the generation of a source list in a manner that does not depend upon a detailed knowledge of the point spread function (PSF) shape; and (5) error analysis. These features make our algorithm considerably more general than previous methods developed for the analysis of X-ray image data, especially in the low count regime. We demonstrate the algorithm's robustness by applying it to various images.Comment: Accepted for publication in Ap. J. Supp. (v. 138 Jan. 2002). 61 pages, 23 figures, expands to 3.8 Mb. Abstract abridged for astro-ph submissio

Spread spectrum-based video watermarking algorithms for copyright protection

Merged with duplicate record 10026.1/2263 on 14.03.2017 by CS (TIS)Digital technologies know an unprecedented expansion in the last years. The consumer can now benefit from hardware and software which was considered state-of-the-art several years ago. The advantages offered by the digital technologies are major but the same digital technology opens the door for unlimited piracy. Copying an analogue VCR tape was certainly possible and relatively easy, in spite of various forms of protection, but due to the analogue environment, the subsequent copies had an inherent loss in quality. This was a natural way of limiting the multiple copying of a video material. With digital technology, this barrier disappears, being possible to make as many copies as desired, without any loss in quality whatsoever. Digital watermarking is one of the best available tools for fighting this threat. The aim of the present work was to develop a digital watermarking system compliant with the recommendations drawn by the EBU, for video broadcast monitoring. Since the watermark can be inserted in either spatial domain or transform domain, this aspect was investigated and led to the conclusion that wavelet transform is one of the best solutions available. Since watermarking is not an easy task, especially considering the robustness under various attacks several techniques were employed in order to increase the capacity/robustness of the system: spread-spectrum and modulation techniques to cast the watermark, powerful error correction to protect the mark, human visual models to insert a robust mark and to ensure its invisibility. The combination of these methods led to a major improvement, but yet the system wasn't robust to several important geometrical attacks. In order to achieve this last milestone, the system uses two distinct watermarks: a spatial domain reference watermark and the main watermark embedded in the wavelet domain. By using this reference watermark and techniques specific to image registration, the system is able to determine the parameters of the attack and revert it. Once the attack was reverted, the main watermark is recovered. The final result is a high capacity, blind DWr-based video watermarking system, robust to a wide range of attacks.BBC Research & Developmen

A guide to time-resolved and parameter-free measures of spike train synchrony

Measures of spike train synchrony have proven a valuable tool in both experimental and computational neuroscience. Particularly useful are time-resolved methods such as the ISI- and the SPIKE-distance, which have already been applied in various bivariate and multivariate contexts. Recently, SPIKE-Synchronization was proposed as another time-resolved synchronization measure. It is based on Event-Synchronization and has a very intuitive interpretation. Here, we present a detailed analysis of the mathematical properties of these three synchronization measures. For example, we were able to obtain analytic expressions for the expectation values of the ISI-distance and SPIKE-Synchronization for Poisson spike trains. For the SPIKE-distance we present an empirical formula deduced from numerical evaluations. These expectation values are crucial for interpreting the synchronization of spike trains measured in experiments or numerical simulations, as they represent the point of reference for fully randomized spike trains.Comment: 8 pages, 4 figure

Robust Transmission of Images Based on JPEG2000 Using Edge Information

In multimedia communication and data storage, compression of data is essential to speed up the transmission rate, minimize the use of channel bandwidth, and minimize storage space. JPEG2000 is the new standard for image compression for transmission and storage. The drawback of Compression is that compressed data are more vulnerable to channel noise during transmission. Previous techniques for error concealment are classified into three groups depending on the Approach employed by the encoder and decoder: Forward Error Concealment, Error Concealment by Post Processing and Interactive Error Concealment. The objective of this thesis is to develop a Concealment methodology that has the capability of both error detection and concealment, be Compatible with the JPEG2000 standard, and guarantees minimum use of channel bandwidth. A new methodology is developed to detect corrupted regions/coefficients in the received Images the edge information. The methodology requires transmission of edge information of wavelet coefficients of the original image along with JPEG2000 compressed image. At the receiver, the edge information of received wavelet coefficients is computed and compared with the received edge information of the original image to determine the corrupted coefficients. Three methods of concealment, each including a filter, are investigated to handle the corrupted regions/coefficients. MATLAB™ functions are developed that simulate channel noise, image transmission Using JPEG2000 standard and the proposed methodology. The objective quality measure such as Peak-signal-to-noise ratio (PSNR), root-mean-square error (rms) and subjective quality Measure are used to evaluate processed images. The simulation results are presented to demonstrate The performance of the proposed methodology. The results are also compared with recent approaches Found in the literature. Based on performance of the proposed approach, it is claimed that the Proposed approach can be successfully used in wireless and Internet communications

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Adaptive and autonomous protocol for spectrum identification and coordination in ad hoc cognitive radio network

The decentralised structure of wireless Ad hoc networks makes them most appropriate for quick and easy deployment in military and emergency situations. Consequently, in this thesis, special interest is given to this form of network. Cognitive Radio (CR) is defined as a radio, capable of identifying its spectral environment and able to optimally adjust its transmission parameters to achieve interference free communication channel. In a CR system, Dynamic Spectrum Access (DSA) is made feasible. CR has been proposed as a candidate solution to the challenge of spectrum scarcity. CR works to solve this challenge by providing DSA to unlicensed (secondary) users. The introduction of this new and efficient spectrum management technique, the DSA, has however, opened up some challenges in this wireless Ad hoc Network of interest; the Cognitive Radio Ad Hoc Network (CRAHN). These challenges, which form the specific focus of this thesis are as follows: First, the poor performance of the existing spectrum sensing techniques in low Signal to Noise Ratio (SNR) conditions. Secondly the lack of a central coordination entity for spectrum allocation and information exchange in the CRAHN. Lastly, the existing Medium Access Control (MAC) Protocol such as the 802.11 was designed for both homogeneous spectrum usage and static spectrum allocation technique. Consequently, this thesis addresses these challenges by first developing an algorithm comprising of the Wavelet-based Scale Space Filtering (WSSF) algorithm and the Otsu's multi-threshold algorithm to form an Adaptive and Autonomous WaveletBased Scale Space Filter (AWSSF) for Primary User (PU) sensing in CR. These combined algorithms produced an enhanced algorithm that improves detection in low SNR conditions when compared to the performance of EDs and other spectrum sensing techniques in the literature. Therefore, the AWSSF met the performance requirement of the IEEE 802.22 standard as compared to other approaches and thus considered viable for application in CR. Next, a new approach for the selection of control channel in CRAHN environment using the Ant Colony System (ACS) was proposed. The algorithm reduces the complex objective of selecting control channel from an overtly large spectrum space,to a path finding problem in a graph. We use pheromone trails, proportional to channel reward, which are computed based on received signal strength and channel availability, to guide the construction of selection scheme. Simulation results revealed ACS as a feasible solution for optimal dynamic control channel selection. Finally, a new channel hopping algorithm for the selection of a control channel in CRAHN was presented. This adopted the use of the bio-mimicry concept to develop a swarm intelligence based mechanism. This mechanism guides nodes to select a common control channel within a bounded time for the purpose of establishing communication. Closed form expressions for the upper bound of the time to rendezvous (TTR) and Expected TTR (ETTR) on a common control channel were derived for various network scenarios. The algorithm further provides improved performance in comparison to the Jump-Stay and Enhanced Jump-Stay Rendezvous Algorithms. We also provided simulation results to validate our claim of improved TTR. Based on the results obtained, it was concluded that the proposed system contributes positively to the ongoing research in CRAHN