Noisy incoherent objects, which are too close to be remotely separated by optically imaging beyond the Rayleigh diffraction limit, might be resolved by employing the Artificial Neural Network (ANN) smart pixel post processing and its mathematical framework, Independent Component Analysis (ICA). It is shown that ICA ANN approach to superresolution based on information maximization principle could be seen as a part of the general approach called space-bandwidth (SW) product adaptation method. Our success is perhaps due to the Blind Source Separation (BSS) Smart-Pixel Detectors (SPD) behind the imaging lens (inverse adaptation), while the Rayleigh diffraction limit remains valid for a single instance of the deterministic imaging systems' realization. The blindness is due to the unknown objects, and the unpredictable propagation effect on the net imaging point spread function. Such a software/firmware enhancement of imaging system may have a profound implication to the designs of the new (third) generation imaging systems as well as other non-optical imaging systems.

FLATLAND is the title of a science fiction story, written in 1880 by E.A. Abbott. The creatures of Flatland, living in their two-dimensional universe, are inspected and manipulated by 3D-people like we are. Here we show how the optics part of this science fiction story can be implemented - for fun and profit.

We present exact results for pulse propagation in a dispersive medium, including the contraction and spreading of the pulse, the covariance between position and wave number and other relevant physical quantities. An analogy is made, both physical and mathematical, describing wave propagation as a collection of particles whose motion is simple. We show that wave motion governed by linear wave equations can be mimicked by particles that move with a constant velocity, but where the velocity is a function of the original position of the particles. Using this picture one can understand the behavior of waves in a simple manner. We also develop the same viewpoint from the perspective of the Wigner distribution. 7

The key to successful ISAR imaging is frequency estimation, as the cross range position of scatteres on the target is determined from the differential Doppler shifts of the received radar signal. Many ISAR images are blurred when conventional processing is used. We show that such blurring can result because the full complexity of the target motion is not taken into account. A sufficiently general model shows that the Doppler shifts are time dependent. We give an example using a quadratic time-frequency method on radar data of an aircraft. Irregular motion is detected, and sharp images are formed in the case where the conventional ISAR processor gave a blurred image. The complexity of the target motion was verified using motion reference data.

It has been shown that often the onset of developing faults in machines is clearly manifest in the time-frequency plane before any problems are noted by conventional methods such as the power spectrum. In this paper we explore a particular feature of some faulting machines, wherein a single vibration frequency briefly and intermittently appears as 'eyelets' in the time-frequency plane. We show that abrupt phase shifts in a tone, or equivalently sudden, rapid changes in the amplitude, cause a transient increase in the instantaneous spectral moments, particularly the instantaneous bandwidth and the instantaneous kurtosis, and cause eyelets in time-frequency similar to those seen in real machine vibrations.

Speech is a signal which is produced as a combination of frication and a quasi periodic train of glottal pulses excites the vocal tract and causes it to resonate. Information is encoded on the signal as the vocal tract changes configuration, resulting in a rapid change of the resonant frequencies. We develop methods, based on differentiation of the short time Fourier transform (STFT) phase, which effectively demodulates the speech signal and produces accurate, high resolution time-frequency estimates of both the resonances and the signal excitation. The method effectively condenses the STFT surface along curves representing the instantaneous frequencies of the vocal tract resonances and the channel group delay function.

Rotation of rotor blades in a helicopter modulates the phase function of radar backscattering, induces frequency modulation on returned signals, and generates side-bands about the center frequency of the helicopter's body Doppler frequency. The modulation induced by rotations can be regarded as a signature of the interaction between the rotor blades and the body of the helicopter, and provides additional information for target recognition complementary to existing recognition methods.

The newly developed Empirical Mode Decomposition (EMD) and the Hilbert Spectral Analysis method will be reviewed. The EMD is an adaptive decomposition with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions. Example of application on the chirp signal form the bat is given to illustrate the potential of the new method.

Successful acoustic signal classification requires the choice of an appropriate problem-adapted signal representation and the extraction of an invariant feature vector for classification. The two scientific core questions however, what is the best signal representation and what is acoustic resemblance, are theoretically still unanswered. Both the definitions of an optimum time-frequency representation (TFD) and of the correct acoustic invariants need some a priori knowledge about the inherent structure and symmetries of the acoustic time series as well as some knowledge about the differences between the classes to be distinguished. In this work, the central parts are a data-driven optimization of the parameterized TFD by maximizing the distance measure of the different sound classes and a geometric similarity concept based on dimensional analysis for defining dimensionless acoustic invariants. Starting from a parameterized TFD of the acoustic signals the joint moments are calculated. Dimensional analysis is used for defining dimensionless invariants under geometric transformations of the TFDs. The significance of these invariants is shown on the basis of the acoustic class of whistling and booming noise (WBN). Using these geometric invariants, the detection rate of WBN can be improved. However, the detection rate is heavily dependent on the chosen TFD. By maximizing the distance measure of the sound classes as a function of two TFD-kernel parameters, the optimum TFD in the sense of the available signal structure can be found and is exemplified by means of an industrial WBN dataset. For validation purpose of the kernel optimization, some acoustic signals in the sense of analytically known asymptotic limit cases with predetermined behavior are given.

The aim of the paper is to present an application of the WT analysis of vibration signals recorded during the run-up or run-down of rotating machinery. Because of complex research work and complicated signals structure the described experiments need an application of special methods. The very good results have been achieved with the use of the WT analysis. However, it demanded special way of synchronization of analysis parameters as well as choice of basis functions. The results of the WT analysis are very interesting, but at the same time their interpretation is very difficult. There is shown an application of the RSL method in the paper. Its application leads up to partitioning of some signal components. This method can be applied to results of the WT analysis, which facilitates the interpretation of scalograms. Identification of these components with diagnostic knowledge is the base of estimation of phenomena occurred during machinery operation thereby technical state of machinery.

In previous work, the spread has been presented as a means to quantify stationarity. This is done by estimating the support of the joint time-frequency correlation function known as the expected ambiguity function. Two fundamental issues concerning the spread are addressed here. The first is that the spread is not invariant under basis transformation. We address this problem by introducing the diagonally optimized spread, based on the proposition that the spread should be calculated using the covariance that is most nearly diagonal under basis transformation. The second issue is that in previous references to spread, the availability of covariance estimates have been assumed, which is an open problem non-stationary processes. A method to provide estimates of locally stationary processes was proposed by Mallat, Papanicolaou and Zhang. In their work they derive a method which calculates the basis which most nearly diagonalize the covariance matrix in the mean square sense. This method is ideally suited to our situation, and we extend it to include calculation of the diagonally optimized spread. The optimally diagonalized spread provides an improved indicator of non-stationarity and illustrates the connections between spread and the diagonizability of the covariance of a random process.

High voltage power equipment have to be designed to withstand a standard lightning impulse voltage of a specified value as a type test for certification. In case of partial or complete failure of the insulation of the equipment, the shape of lightning impulse undergoes a change. In order to compute the time/frequency characteristics of such impulse voltage,the wavelet transform technique has been used. The standard, chopped and modified impulse voltages have been generated using a computer program. The various voltage/time magnitudes have been used for determination of time/frequency characteristics for a number of dilation coefficients 'a.' The values such obtained are normalized and typical values are plotted, to show the specific differences. It is inferred that there exists a threshold value of dilation constant, bellow which perturbations in the voltage waveshape/time becomes difficult to detect. The paper deals with the limitations of such method and the lowest value of dilation coefficient to be considered for the use in such analysis.

In this paper we introduce a feature set for texture segmentation, based on an extension of fractal dimension features. Fractal dimension extracts roughness information from images considering all available scales at once. In this work a single scale is considered at a time so that textures that do not possess scale invariance are sufficiently characterized. Single scale features are combined with multiple scale features for a more complete textural representation. Wavelets are employed for the computation of single and multiple scale roughness features due to their ability to extract information at different resolutions. Features are extracted at multiple directions using directional wavelets, and the feature vector is finally transformed to a rotational invariant feature vector that retains the texture directional information. An iterative K-means scheme is used for segmentation. The use of the roughness feature set results in high quality segmentation performance. The feature set retains the important properties of fractal dimension based features, namely insensitivity to absolute illumination and contrast.

Aiming at the demand of adaptive wavelet transforms via lifting, a three-stage lifting scheme (predict-update-adapt) is proposed according to common two-stage lifting scheme (predict-update) in this paper. The second stage is updating stage. The third is adaptive predicting stage. Our scheme is an update-then-predict scheme that can detect jumps in image from the updated data and it needs not any more additional information. The first stage is the key in our scheme. It is the interim of updating. Its coefficient can be adjusted to adapt to data to achieve a better result. In the adaptive predicting stage, we use symmetric prediction filters in the smooth area of image, while asymmetric prediction filters at the edge of jumps to reduce predicting errors. We design these filters using spatial method directly. The inherent relationships between the coefficients of the first stage and the other stages are found and presented by equations. Thus, the design result is a class of filters with coefficient that are no longer invariant. Simulation result of image coding with our scheme is good.

Over the past several years, the Naval Research Laboratory has been developing video inspection systems for assessing the coatings condition in shipboard ballast tanks. Two prototype systems have been configured and are presently being utilized to perform video inspections of dry and filled ballast tanks. These systems are described in this paper. The large size and low level lighting associated with this application results in 'noisy' imagery. A wavelet based de-noising method has been developed that removes the noise in the video imagery while maintaining other edges important to corrosion detection. Specific examples that demonstrate the efficacy of the de-noising methods are provided. Wavelet edge detection methods are then applied to the de-noised imagery to identify both regions of potential rust and the spatial distribution of rust. Additional methodologies are then utilized for final corrosion classification. The paper will provide examples of imagery collected in shipboard ballast tanks and examples of applying the automatic corrosion detection algorithms. These examples demonstrate the algorithms ability to work with 'noisy' imagery and to ignore objects in the imagery such as ladders and pipes. They also demonstrate the robustness of the developed automatic corrosion detection algorithms.

We described an adaptive denoising method to improve image quality in a wavelet-based image compression process that uses dithered quantization. In our method, the second-order moment of the quantization noise is made independent of the signal by random quantization. Then, the quantization noise is reduced by thresholding wavelet coefficients. We first obtained a fixed threshold using any known technique. Then, a neighborhood is searched for the optimal threshold to optimize some cost function.

Chirps (i.e., transient AM-FM waveforms) are ubiquitous in nature and man-made systems, and they may serve as a paradigm for many nonstationary deterministic signals. The time-frequency plane is a natural representation space for chirps, and we will here review a number of questions related to chirps, as addressed from a time-frequency perspective. Global and local approaches will be described for matching and/or adapting representations to chirps. As a corollary, joint time-frequency descriptions of chirps will be shown to allow for effective definitions of instantaneous frequencies via localized trajectories on the plane. A number of applications will be mentioned, ranging from bioacoustics to turbulence and gravitational waves.

A hybrid algorithm is proposed for very low bit-rate video compression. The algorithm uses a new wavelet based coder for Intraframe compression and DCT for Interframe compression. The wavelet coder technique known as OBTWC (Overlapped Block Transform Wavelet Coder) consists of three steps. First, a set of overlapped block transforms is used to transform the image data into 8 X 8 blocks in the frequency domain. Second, a mapping is then performed to convert the transformed image into a multiresolution representation that resembles the zero- tree wavelet transform. Third, the multiresolution representation is then coded by a conventional dyadic wavelet coder, which basically truncates the high frequency contents in a very efficient manner. Our proposed method essentially combines the advantages of both block transform and wavelet coding techniques while eliminating their respective weaknesses. Simulation results show that the coder achieves more than 300:1 compression ratio at a frame rate of 10 per second.

This paper presents a wavelet-based image coder that is optimized for transmission over binary channels with memory. The proposed coder uses a channel-optimized trellis-coded quantizer (COTCQ) designed for a binary first-order Markov channel. The quantizer stage exploits the channel memory by incorporating the characteristics of the additive correlated channel noise during the quantizer design and by using a new trellis structure. The performance of the proposed memory-optimized COTCQ (MCOTCQ) image coding system is presented for different bit error probabilities and noise correlation parameters. It is shown that the performance of the coder is improved significantly when the second-order statistics of the noise are incorporated at the quantizer design level.

In this paper we propose a subband image compression by using wavelet transform to split original images. Each of subband images is then quantized by an adaptive vector quantization with dynamic bit allocation based on advantage of nature of wavelet coefficients. The energy of each subband image, except the lowest frequency subband image will not be quantized, will be sorted from minimum to maximum. Energy of each subband image is calculated to allocate bits not over the desired bit rate. The accumulation of energy from these subband images will be divided into 4 groups. First two lower energy groups will be encoded with 256 and 1 6 code vectors for 1 6 pixels block size in accordance with energy ratio. Others will be encoded with 256 code vectors for 4 and 16 pixels block size. Based on the given bit rate, the total dynamical bit rate of each group is calculated. If the total dynamical bit rate in the group is less or more than the given bit, it will thenbe adjusted based on the energy of subband image in only the same group. The remaining of energy from higher energy group will be carried to lower. The experiments are shown that the resulting images from the proposed method can be clearly improved by Peak Signal to Noise Ratio (PSNR) of 36.30 16, MSE =15.2377, 1 .03 125 bpps.

In portable communication devices there is a strong incentive to extend battery life through reduced power consumption of all system elements. This paper proposes a novel integration of image decompression and passive-matrix liquid crystal display driving through the application of DWT methods to the field of Multiple Line Addressing (MLA). This eliminates for the first time the need for data conversion between the decoded image and a format suitable for input to the display drivers. This is achieved by exploiting an inherent property of the liquid crystal to perform a 1-D inverse wavelet transform on the compressed incoming data. The paper presents a comparison of system performance for different wavelets, taking into account image compression rates, display performance and circuit complexity. It also presents a detailed system architecture and a discussion of the benefits and possible applications for such a scheme.

We present a framework for the use of stationary phase approximations to a Morlet wavelet transform as a device to generate computationally efficient algorithms for extracting modulation information in frequency modulated (FM) signals. Presented here are two specific FM estimators generated from this approach that may be implemented in terms of filter banks with very few filters.

The online system, plasmo process observer, enables observation of plasma created by e.g. laser welding in two frequency bands, visible and near infrared. The system offers the feature of online detection of failures like pores and enables the user to store the measured data in databases. This paper deals with both aspects. First the application of wavelets for data preprocessing as a first step of online classification of failures is introduced. This time scale-analysis is compared to standard algorithms in frequency or time domain like DFT or digital filters respectively. The second part of this paper shows the capabilities of wavelets for data compression. This is necessary due to the large amount of data generated by the system. It is shown how important data can be extracted of noisy signals by using wavelets. The process observer has been successfully implemented in welding and drilling applications for automotive and aerospace industry with a very high recognition rate of all defects.

For decades the process of aluminum electrolysis has facilitated the production of aluminum. The process occurs within aluminum electrolytic cells, where alumina (Al₂O₃) is dissolved in liquid cryolite (Na₃AlF₆). The dissolved alumina is reduced by the carbon anode and forms carbon dioxide. Complexes containing aluminum ions migrate to the cathode surface (bath-metal interface) where aluminum metal is produced. The monitoring of the electrolysis process is done through the use of the cell resistance. Using resistance set point values that are indirectly related to the desired alumina concentration in the bath (cryolite), the computed resistance can indicate if the cell is operating within acceptable production conditions. The resistance time series is a nonstationary random process. We have applied the principal component method to shortsegments of each time series to identify key components. However the principal components are data dependent. In order to study the time series' localized structure we use a wavelet packet based approach to analyze this nonstationary process. We use Daubechies 3 orthonormal wavelet and scaling function as our basis functions and model each short segment of the resistance time series as a locally stationary wavelet process. The use of wavelet packets increases the separability of the innovations into individual packets. Hence each wavelet packet time series represents a single subprocess. The analysis of individual subprocesses yields information for making inference of how the process evolves during unstable operating conditions.

Lossless compression techniques are essential in archival and communication of large amounts of homogeneous data in radiological image databases. This paper exploits dependencies that exist between the pixel intensities in three dimensions to improve compression for a set of similar medical images. These 3-D dependencies are systematically presented as histograms, plots of wavelet decomposition coefficients, feature vectors of wavelet decomposition coefficients, entropy and correlation. This 3-D dependency is called set redundancy for medical image sets. Predictive coding is adapted to set redundancy and combined with integer wavelet transformations to improve compression. This set compression improvement is demonstrated with 3-D sets of magnetic resonance (MR) brain images.

The concern of the blind source separation problem is to extract the underlying source signals from a set of their linear mixtures, where the mixing matrix is unknown. It was discovered recently, that use of sparsity of source representation in some signal dictionary dramatically improves the quality of separation. In this work we use the property of multiscale transforms, such as wavelet or wavelet packets, to decompose signals into sets of local features with various degrees of sparsity. We use this intrinsic property for selecting the best (most sparse) subsets of features for further separation. Experiments with simulated signals, musical sounds and images demonstrate significant improvement of separation quality.

Hyperspectral remote sensing by air platforms can passively generate over two hundred channels of images of terabyte data the ground surface reflectance/eminence simultaneously, with wavelength ranging from 0.4 to 2.5 micrometers and to include a full infrared spectrum. We have extended the hyperspectral to include RF spectral for both the foliage penetration (from L band 1 GHz to UHF band 0.5 GHz,) using the polarization RF features and the terrain location ID for automatic navigation registration. These generalizations are possible because we have based our design of the foliage penetration (FOPEN) Interferometric Synthetic Aperture Radar (IFSAR) on all digital transceiver array and Field Programmable Gate Arrays (FPGA). We are able to do that, since we have leveraged the ONR 100 dB Digital Array Radar (DAR) for shipboard volume search radar (VSR) using the matured & rugged GaAs cellular phone technology. We study whether the high dynamic range DAR VSR approach can overcome the long baseline terran curvature (that might otherwise not be suited for the FOLPEN low frequency IFSAR). We show the standard deviation of the phase digital resolution better then 1o might overcome the terrain curvature due to low frequency, and long time integration. The applications of this technology include environmental monitoring and mineral exploration and mining, communication and Aided Target Recognition (ATR). The hyperspectral imagery takes the advantage of more unique spectral signature in terms of the massively parallel artificial neural network computation using the unsupervised learning Independent Component Analyses (ICA) algorithm introduced to the Landsat by Szu. The supervised classification is based on the library of spectral signals of known object material characteristics using various constrained versions of the orthogonal subspace projections (OSP) by. In this paper, we combine both the supervised OSP and the unsupervised ICA hyperspectral imaging algorithms. Then, we present all digital version of FOPEN SAR, considered as one of RF channels in ultraspectral image processing. Taking the advantage of the high dynamic range ONR DAR VSR technology, we can measure both RF signatures and 3D terrain by means of Interferometric (IF) FOPEN SAR. We prefer a real-time one-path fly over using bi-static Interferometric SAR equipped with a Stokes polarization vector information that can provide us with not only the RF signatures but also terrain height for location ID (knowing terran contour map stored in the flight data basis). Such an ultraspectral imaging feature-fusion system can manage Forrest search and rescue when it is complement IFSAR FOPEN with high-resolution EO/IR signatures. Conclusion and discussion are given in the final section.

A high performance, fully digital Foliage Penetrating Synthetic Aperture Radar (FOPEN SAR) system is described. The FOPEN SAR algorithm is illustrated using Matlab. Digital implementation is derived and simulated using VHDL. The complex mathematical functions required by the algorithm have been demonstrated. Simulations have achieved an SNR equals 290 dB when compared to the baseline results from Matlab. The accuracy of the simulation was limited by the resolution of certain trigonometric and exponential functions implemented using VHDL, and thus can be improved upon. This would allow greater flexibility between speed/area considerations without degradation of the target resolution (100dB-signal accuracy).

This novel feature-based method is able to reduce the computation overheads without compromising the matching accuracy of satellite images. It incorporates the bi-orthogonal wavelet filter using B-splines designed by Yu and Ho. The bi-orthogonal wavelet filter is used to perform multi-resolution edge extraction and multi-resolution matching. Edges are matched using adaptive matching windows that vary their shapes according to the directions of the edges. An adaptive searching range is applied because the searching range of each edge point may be different. Moreover, the matched results for low resolution levels are utilized for interpolating high resolution mismatched pixels. Detailed comparison with other new feature-based algorithm on SPOT and aerial stereo images was performed. The results obtained show that the proposed algorithm was computationally more efficient as well as achieving an overall improved matched accuracy.

Whether the Sun has significantly influenced the climate during the last century has been under extensive debates for almost two decades. Since the solar irradiance varies very little in a solar cycle, it is puzzling that some geophysical parameters show proportionally large variations which appear to be responding to the solar cycles. For example, variation in low-altitude clouds is shown correlated with solar cycle, and the onset of Forbush decrease is shown correlated with the reduction of the vorticity area index. A possible sun-climate connection is that galactic cosmic rays modulated by solar activities influence cloud formation. In this paper, we apply wavelet transform to satellite and surface data to examine this hypothesis. Data analyzed include the time series for solar irradiance, sunspots, UV index, temperature, cloud coverage, and neutron counter measurements. The interactions among the elements in the Earth system under the external and internal forcings give out very complex signals. The periodicity of the forcings or signals could range widely. Since wavelet transforms can analyze multi-scale phenomena that are both localized in frequency and time, it is very useful techniques for detecting, understanding and monitoring climate changes.

Wavelet-based image registration has previously been proposed by the authors. In previous work, maxima obtained from orthogonal Daubechies filters as well as from Simoncelli steerable filters were utilized and compared to register images with a multi-resolution correlation technique. Previous comparative studies between both types of filters have shown that the accuracy obtained with orthogonal filters seemed to degrade very quickly for large rotations and large amounts of noise, while results obtained with steerable filters appeared much more stable under these conditions. In other studies based on the use of mutual information for image registration, several authors have shown that maximizing mutual information enables one to reach sub-pixel registration accuracy. In this work, we are utilizing Simoncelli steerable filters to provide the basic data from which mutual information is maximized and we are applying this method to remotely sensed imagery.

Applications such as Unmanned Air or Land Vehicles (UAVs) depend on good quality image data to assist in navigation and other tasks or decisions. In the real world environments, atmospheric conditions can lead to degradation of images and the occlusion or distortion of objects of interest in images. This work will look at techniques that can be used to both determine the type and amount of atmospheric conditions present in image data. This information could then be used by our previously developed system to assist in the reduction of atmospheric effects.

A new wavelet based image coder is proposed for SAR image compression. The coding technique known as OBTWC (Overlapped Block Transform Wavelet Coder) consists of three steps. First, a set of overlapped block transforms is used to transform the image data into 8 X 8 blocks in the frequency domain. Second, a mapping is then performed to convert the transformed image into a multiresolution representation that resembles the zero-tree wavelet transform. Third, the multiresolution representation is then coded by a conventional dyadic wavelet coder, which basically truncates the high frequency contents in a very efficient manner. Our proposed method essentially combines the advantages of both block transform and wavelet coding techniques while eliminating their respective weaknesses. The image compression algorithm was applied to SAR images supplied by Air Force, Army, and NASA. The compression performance in terms of Peak Signal-to-Noise Ratio is better than that of a commercial wavelet coder in the market.

An ISAR image formation approach has been developed that incorporates advanced imaging and exploitation techniques for non-cooperative moving target feature extraction and ATR. A unique signal based motion compensation algorithm has been developed that works for both SAR and ISAR. Advanced Time-frequency (T-F) processing has been incorporated, which includes both slow time-Doppler frequency and fast time-RF.

Using salient features to drive image filtering is an important problem in image analysis and computer vision. The notion of a scale space has as a result gained popularity on account of its advantage in providing a dynamic description of image features. Object or shape information is inherently contained in level sets or level curves of an image, and its preservation while removing noise can be done reliably through processing of level sets of an image instead of directly working on its intensity values. Following this argument, and the fact that SAR images are impulsive in nature, we propose a level-set-based multiresolution filtering technique for segmentation of SAR imagery. Extracted target information of images, from various radar view angles are integrated to build up an overall target silhouette, which is then used for classification of two main target vehicle types.

Based on the point scatterer model, the radar signal can be effectively analyzed using the joint time-frequency (JTF) method. The basis functions of a few primary point scatterers are believed to carry target motion information essential to the ISAR imaging process. One major problem with the JTF method is the computation load associated with the exhaustive search process for motion parameters. In this paper, genetic algorithms (GA) are used to for the parameterization process in the JTF method. Real and binary coded GA are investigated and their performance compared with the exhaustive search. It is shown that a significant amount of time can be saved while achieving almost the same image quality by using real-coded GA.

This paper first reviews some basic properties of the discrete chirp-Fourier transform and then present an adaptive chirp- Fourier transform, a generalization of the amplitude and phase estimation of sinusoids (APES) algorithm proposed by Li and Stoica for sinusoidal signals. We finally applied it to the ISAR imaging of maneuvering targets.

This research deals with finite length, perfect reconstruction two-channel orthonormal wavelet filters. We have previously derived equations that allow the user to set the regularity of these filters to any value between one and the maximum possible. These equations were extremely involved and intricate. We derive identities that greatly simplify the equations and reduced computational complexity. We indicate how the equations may be used to find the optimum filter for a particular application over a pool of filters of regularity set by the user. We advance conjectures as to the theoretical significant of the structure of these equations and discuss numerical solutions.

A survey of known wavelet groups is listed and properties of the symmetrical first-order hyperbolic wavelet function are studied. This new wavelet is the negative second derivative function of the hyperbolic kernel function, [sech((beta) (theta) )]ⁿ where n equals 1, 3, 5,... and n equals 1 corresponds to the first-order hyperbolic kernel, which was recently proposed by the authors as a useful kernel for studying time-frequency power spectrum. Members of the 'crude' wavelet group, which includes the hyperbolic, Mexican hat (Choi-Williams) and Morlet wavelets, are compared in terms of band-peak frequency, aliasing effects, scale limit, scale resolution and the total number of computed scales. The hyperbolic wavelet appears to have the finest scale resolution for well-chosen values of (beta)