Image segmentation in the wavelet domain using N-cut framework

We introduce a wavelet domain image segmentation algorithm based on Normalized Cut (NCut) framework in this thesis. By employing the NCut algorithm we solve the perceptual grouping problem of image segmentation which aims at the extraction of the global impression of an image. We capitalize on the reduced set of data to be processed and statistical features derived from the wavelet-transformed images to solve graph partitioning more efficiently than before. Five orientation histograms are computed to evaluate similarity/dissimilarity measure of local structure. We use properties of the wavelet transform filtering to capture edge information in vertical, horizontal and diagonal orientations. This approach allows for direct processing of compressed data and results in faster implementation of NCut framework than that in the spatial domain and also decent quality of segmentation of natural scene images

The development of the quaternion wavelet transform

The purpose of this article is to review what has been written on what other authors have called quaternion wavelet transforms (QWTs): there is no consensus about what these should look like and what their properties should be. We briefly explain what real continuous and discrete wavelet transforms and multiresolution analysis are and why complex wavelet transforms were introduced; we then go on to detail published approaches to QWTs and to analyse them. We conclude with our own analysis of what it is that should define a QWT as being truly quaternionic and why all but a few of the “QWTs” we have described do not fit our definition

Blind Yield Detection in Steel Structure for Automatic Nondestructive Testing Using Ultrasonic Sensors

Detection of yield zones using nondestructive testing (NDT) technology for assessing the structural integrity of the existing steel buildings/bridges is extremely important. The average energy over the “effective echoes” (in “good” signal quality) is a robust feature for the yield detection in steel structures. Nevertheless, this average-energy feature extraction requires rigorous manual data-acquisition and human operation. Therefore, in this thesis, we make the first-ever attempt to design a totally-blind and automatic steel-structure yielddetection mechanism, which requires neither the a priori information about the signal nor the human effort in calibration, operation, or data analysis. This new scheme is built upon a robust preprocessor, which involves both blind-signature-signal-extraction and zero-crossingrate thresholding, to identify the starting and terminal time points of each ultrasonic echo. Thus, the new computer-aided system can easily estimate the signal-to-noise ratios and automatically extract the effective echoes to calculate the corresponding average energy. The performance reflected by the receiver-operating characteristic (ROC) curves of the proposed method is very close to that of the conventional human-operating technique. Hence one may save much human effort in the sacrifice of very little detection accuracy by using our proposed new system

Joint bit allocation and precoding for filterbank transceivers in NOFDM systems

Recently, the non orthogonal frequency division multiplexing (NOFDM) systems have attracted increased interest. They have several advantages over traditional OFDM systems: higher bandwidth efficiency; reduced sensitivity to carrier frequency offsets, oscillator phase noise and narrowband interference; and reduced intersymbol/intercarrier interference (ISI/ICI). In particular, low ISI/ICI will be important for future systems where Doppler frequencies will be larger (equivalently, channel variations will be faster) due to higher carrier frequencies and higher mobile velocities. In the first part of this thesis the duality of multicarrier systems and Gabor frames is discussed and applied to the design of a generalized multicarrier system based on a filterbank structure. The efficient polyphase implementation is also discussed. In this thesis the channel capacity of a GMC systems is evaluated through the diagonalization of an equivalent matrix model where intersymbol and intercarrier interferences have been included. Exploiting the majorization theory, the mutual information can be represented as a Schur-concave function and it is maximized through a joint transceiver design adding a linear precoder at the transmitter and a LMMSE equalizer at the receiver. The capacity is derived by the eigenvalue decomposition of the global system matrix including the noise colored by the receiver filtering and employing a power allocation of the transmitted power according to the well-known water-filling solution. This thesis investigates also the behaviour of the NOFDM systems when a power and bit allocation algorithm (like the Campello one) is employed in order to satisfy a certain QoS constrain. A comparison of the performances with OFDM systems is included. Finally a simple application of the cognitive radio paradigm employing filterbankbased multicarrier systems is developed and some interesting results are showed

An Investigation of Orthogonal Wavelet Division Multiplexing Techniques as an Alternative to Orthogonal Frequency Division Multiplex Transmissions and Comparison of Wavelet Families and Their Children

Recently, issues surrounding wireless communications have risen to prominence because of the increase in the popularity of wireless applications. Bandwidth problems, and the difficulty of modulating signals across carriers, represent significant challenges. Every modulation scheme used to date has had limitations, and the use of the Discrete Fourier Transform in OFDM (Orthogonal Frequency Division Multiplex) is no exception. The restriction on further development of OFDM lies primarily within the type of transform it uses in the heart of its system, Fourier transform. OFDM suffers from sensitivity to Peak to Average Power Ratio, carrier frequency offset and wasting some bandwidth to guard successive OFDM symbols. The discovery of the wavelet transform has opened up a number of potential applications from image compression to watermarking and encryption. Very recently, work has been done to investigate the potential of using wavelet transforms within the communication space. This research will further investigate a recently proposed, innovative, modulation technique, Orthogonal Wavelet Division Multiplex, which utilises the wavelet transform opening a new avenue for an alternative modulation scheme with some interesting potential characteristics. Wavelet transform has many families and each of those families has children which each differ in filter length. This research consider comprehensively investigates the new modulation scheme, and proposes multi-level dynamic sub-banding as a tool to adapt variable signal bandwidths. Furthermore, all compactly supported wavelet families and their associated children of those families are investigated and evaluated against each other and compared with OFDM. The linear computational complexity of wavelet transform is less than the logarithmic complexity of Fourier in OFDM. The more important complexity is the operational complexity which is cost effectiveness, such as the time response of the system, the memory consumption and the number of iterative operations required for data processing. Those complexities are investigated for all available compactly supported wavelet families and their children and compared with OFDM. The evaluation reveals which wavelet families perform more effectively than OFDM, and for each wavelet family identifies which family children perform the best. Based on these results, it is concluded that the wavelet modulation scheme has some interesting advantages over OFDM, such as lower complexity and bandwidth conservation of up to 25%, due to the elimination of guard intervals and dynamic bandwidth allocation, which result in better cost effectiveness

Wavelet and Multiscale Methods

Various scientific models demand finer and finer resolutions of relevant features. Paradoxically, increasing computational power serves to even heighten this demand. Namely, the wealth of available data itself becomes a major obstruction. Extracting essential information from complex structures and developing rigorous models to quantify the quality of information leads to tasks that are not tractable by standard numerical techniques. The last decade has seen the emergence of several new computational methodologies to address this situation. Their common features are the nonlinearity of the solution methods as well as the ability of separating solution characteristics living on different length scales. Perhaps the most prominent examples lie in multigrid methods and adaptive grid solvers for partial differential equations. These have substantially advanced the frontiers of computability for certain problem classes in numerical analysis. Other highly visible examples are: regression techniques in nonparametric statistical estimation, the design of universal estimators in the context of mathematical learning theory and machine learning; the investigation of greedy algorithms in complexity theory, compression techniques and encoding in signal and image processing; the solution of global operator equations through the compression of fully populated matrices arising from boundary integral equations with the aid of multipole expansions and hierarchical matrices; attacking problems in high spatial dimensions by sparse grid or hyperbolic wavelet concepts. This workshop proposed to deepen the understanding of the underlying mathematical concepts that drive this new evolution of computation and to promote the exchange of ideas emerging in various disciplines

Blind Estimation of Multi-Path and Multi-User Spread Spectrum Channels and Jammer Excision via the Evolutionary Spectral Theory

Despite the significant advantages of direct sequence spreadspectrum communications, whenever the number of users increases orthe received signal is corrupted by an intentional jammer signal,it is necessary to model and estimate the channel effects in orderto equalize the received signal, as well as to excise the jammingsignals from it. Due to multi-path and Doppler effects in thetransmission channels, they are modeled as random, time-varyingsystems. Considering a wide sense stationary channel during thetransmission of a number of bits, a linear time-varying modelcharacterized by a random number of paths, each beingcharacterized by a delay, an attenuation factor and a Dopplerfrequency shift, is shown to be an appropriate channel model. Itis shown that the estimation of the parameters of such models ispossible by means of the spreading function, related to thetime-varying frequency response of the system and the associatedevolutionary kernels. Applying the time-frequency orfrequency-frequency discrete evolutionary transforms, we show thata blind estimation procedure is possible by computing thespreading function from the discrete evolutionary transform ofthe received signal. The estimation also requires the synchronizedpseudo-noise sequence for either of the users we are interestedin. The estimation procedure requires to adaptively implementingthe discrete evolutionary transform to estimate the spreadingfunction and determine the channel parameters. Once the number ofpaths, delays, Doppler frequencies and attenuations characterizingthe channel are found, a decision parameter can be obtained todetermine the transmitted bit. We will show also that ourestimation approach supports multiuser communication applicationssuch as uplink and downlink in wireless communicationtransmissions. In the case of an intentional jamming, common inmilitary applications, we consider a receiver based onnon-stationary Wiener masking that excises such jammer as well asinterference from other users. Both the mask and the optimalestimator are obtained from the discrete evolutionarytransformation. The estimated parameters from the computedspreading function, corresponding to the closest to the line ofsight signal path, provide an efficient detection scheme. Ourprocedures are illustrated with simulations, that display thebit-error rate for different levels of channel noise and jammersignals