In many parts of the world, breast cancer is the leading cause mortality among women and it is the major cause of cancer death, next only to lung cancer. In recent years, microwave imaging has shown its potential as an alternative approach for breast cancer detection. Although advances have improved the likelihood of developing an early detection system based on this technology, there are still limitations. One of these limitations is that target responses are often obscured by surface reflections. Contrary to ground penetrating radar applications, a simple reference subtraction cannot be easily applied to alleviate this problem due to differences in the breast skin composition between patients. A novel surface removal technique for the removal of these high intensity reflections is proposed in this paper. This paper presents an algorithm based on the multiplication of adjacent wavelet subbands in order to enhance target echoes while reducing skin reflections. In these multiscale products, target signatures can be effectively distinguished from surface reflections. A simple threshold is applied to the signal in the wavelet domain in order to eliminate the skin responses. This final signal is reconstructed to the spatial domain in order to obtain a focused image. The proposed algorithm yielded promising results when applied to real data obtained from a phantom which mimics the dielectric properties of breast, cancer and skin tissues.
We evaluated two random number generator algorithms using first-order and second-order chaotic maps. The first algorithm, which is based on the central limit theorem, allows us to approximate a Gaussian random variable as the sum of a given chaotic sequence. We considered two first-order maps (Bernoulli, Tent) and two second-order maps (Logistic, and Quadratic). In each instance, we verified that the sequence of random numbers had kurtosis of 3. In the case of the Bernoulli map, we determined that the statistical independence of samples is dependent on the map parameter B. The second algorithm, which is based on Von Neumann's Method, allowed us to reject samples from a chaotic sequence with uniform distribution to obtain a Gaussian distribution within a specific range (U, V). For the first-order maps, we estimated their probability density function in this range and computed deviations from the theoretical Gaussian density. In summary, we determined that samples generated via these two algorithms satisfied statistical tests for normal distributions, thus demonstrating that chaotic maps can be effectively to generate Gaussian samples.
Classical work in the field of high-resolution radar often assumes that an echo signal is made of a number of components that can be decomposed via Fourier analysis. Adjacent components are said to be resolved in the frequency domain if the intensity between them drops at least 3 decibels. This working definition is an extension of Lord Rayleigh's criterion for optical resolution. The problem with this approach is that whereas Rayleigh's criterion assumes signal incoherence, thus allowing for the addition of power components, a high-resolution radar signal is often the coherent sum of sinusoids, which implies voltage addition. The purpose of this paper is to discuss the consequences of using Rayleigh's criterion in the analysis of radar signals. Specifically, computer simulations using a complex signal are analyzed via the periodogram as the relative phase between the two components of the signal is allowed to change. The net effect introduced by this phase variation is to reduce or increase the spacing and intensity between two adjacent spectral peaks. These changes are due to constructive or destructive interference of spectral cross terms that cannot be ignored when attempting to resolve frequency components from one another. For instance, the simulations show that when using the averaged periodogram, the intensity in-between two adjacent components is above the -3 decibel threshold for a phase range of 1.2π radians, although the standard resolution criterion of c/2β is satisfied. Similar results are obtained when using a number of windows that are known to control sidelobe levels. Thus, the use of Rayleigh's criterion to define the resolution of a high-resolution radar system is technically inconsistent and undermines our ability to perform quantitative comparisons of target profiles, Doppler profiles and range-Doppler images. In this light, the authors promote the adoption of alternative criteria for judging resolution gains based on the norm of the signal in the (spatial) frequency domain.
We explore the characteristics of chaos for wideband radar imaging. Chaos can be generated via non-linear functions that produce statistically independent samples with invariant probability density functions. By feeding this type of chaos to the input of a voltage-controlled oscillator, a stochastic frequency modulated signal with fractal features is generated. The FM signal is an ergodic and stationary process with initial random phase. The power spectral density of such signal is typically broadband. We show that the time autocorrelation associated with the FM signal provides high range resolution for zero Doppler and dies out rapidly for increasing Doppler shifts. Furthermore, we show that a set of realizations of the signal can be processed into a set of ambiguity surfaces that when averaged yield a low self-noise pedestal.
Time-frequency techniques have been successfully used in the analysis of non-stationary signals. Several approaches have been proposed that address concerns such as Time-Frequency (TF) resolution and the elimination of cross-terms. In this work, a TF technique based on the use of Spatially Variant Apodization (SVA) is introduced that focuses on the detection of non-stationary signals that consists of several components that have different amplitudes. The SVA approach is applied to the Short-Time Fourier Transform (STFT) to detect small intensity components that are buried in high sidelobes of other components. Resolution using the SVA is better than the resolution obtained using the STFT with non-rectangular windows. Synthesis can be performed using the overlap-add method. Because of the implementation of the SVA, the modified STFT using sidelobe apodization can have good resolution, detect small intensity components, and show no cross terms in the TF plane, given that stationarity can be assumed using an appropriate window length in the STFT.
SAR/ISAR image processing involves a two-dimensional Fourier transform that may produce significant high intensity sidelobes which obscure low intensity scatterers in the image. Spatially variant sidelobe apodization is a technique that reduces sidelobe levels in a final Fourier image while maintaining the image resolution that would be obtained using the rectangular window. In this paper, a generalization of this technique based on the use of different parametric windows is proposed. Low sidelobe levels are obtained at the expense of increasing the complexity of the sidelobe apodization algorithm. Similar resolution and lower sidelobe levels were obtained using a one-dimensional example when compared to the spatially variant apodization technique. The method was also tested and results are shown when using this new sidelobe apodization technique with a two dimensional ISAR image.
An approach is presented for the design of time-varying filters that separate selected ISAR target signatures with a constant false alarm rate. Here, the time-frequency representation of each signature is utilized to define a binary filter which is enhanced and labeled using computer vision techniques. Upon filtering, the signatures of the targets are synthesized from their Short Time Fourier Transform representations. In order to obtain a focused radar image for each target, its filtered signature must be motion compensated in the frequency domain. Therefore, radar images can be generated for scenarios in which multiple moving targets can not be imaged otherwise. As an instance, the response of a stepped frequency radar system is simulated to demonstrate that combined signatures of aircraft are effectively separated, compensated and processed into individual images.
We describe an approach for inverse synthetic aperture radar (ISAR) imaging based on the Gabor wavelet transform. The Gabor basis function introduces three signal parameters which allow the components of a target signature to be mapped into a three-dimensional domain. Time, range, and frequency constitute the dimensions of this domain. Component distribution over the range and frequency dimensions corresponds to a snap shot of the target's scattering centers at a particular observation time. The snap shot resolution can be adjusted in each dimension by properly selecting the Gabor wavelet parameters. Parameter selection, as discussed in this paper, is used to minimize the quadratic phase distortion associated with moving target components. For multiple targets experiencing different velocities, selective motion compensation is incorporated to the Gabor wavelet transform approach, thus yielding focused imagery.
In SAR/ISAR imaging, estimation of motion parameters of moving objects is needed in order to compensate for translational motion that causes image blurring. Phase parameter estimation from signals corresponding to one scatterer buried in complex white Gaussian noise is a problem for which various successful techniques have been devised. For multicomponent signals, it is difficult to use these parametric methods. Isolating the signal's components in order to do the estimation can help. The authors have previously proposed the isolation of scatterers for instantaneous frequency estimation. This process allows not only the extraction of components but also the manipulation of each object separately. In this paper, we study the use of time-frequency filtering on parameter estimation for a complex exponential signal with polynomial phase modulation. Our study is limited to the use of the Discrete Polynomial- Phase Transform (DPT) of Peleg and Friedlander. Our approach is to simplify the problem of parameter estimation from multicomponent signals by isolating them and then performing the estimation on each one separately. The process of isolating components is also shown to be improved by applying superresolution in the computation of the time- frequency representation. We also formulate an approach using the DPT for motion parameter estimation on a signal model for stepped-frequency ISAR returns from a scatterer.
In previous work, the authors have proposed the compensation of translational motion of an object via time-frequency filtering in a way that separation of scatterers can be done and compensation can be achieved selectively. In this paper, the effect of filtering in the time-frequency domain is studied focusing on the effects that this processing introduces to the phase of the scatterer response. The instantaneous frequency associated with one scatterer in the image is estimated and compared to the estimated frequency obtained for the case where only that scatterer is present by itself. Deviations caused by these two computations are presumed to affect the final compensation of an image regardless of which compensation technique is used.
Several methods have been proposed for motion parameter estimation and motion compensation in SAR/ISAR images. Some of the methods work using the information from a prominent scatterer and may require that it be well isolated. In order to extract part of an image for selective motion compensation, a filtering process must take place and in this paper, we propose to filter the range profile information. We apply and extend some concepts and techniques from time-frequency analysis to range profile formation and processing. In particular, we use time-varying filtering to accomplish our goal of selecting and separately processing a component of the image information that represents an object with different motion than other parts of the image. We also consider the option of using a superresolution method that enhances the resolution of the short-time Fourier transform to improve the accuracy of the filtering process. The system that is considered for simulations is a stepped-frequency ISAR. Even though our application is motion compensation, this paper also serves to apply and improve time-frequency processing techniques for use in SAR/ISAR imaging.
Signal separation or editing of components in the time-frequency domain remains an important problem that is equivalent to time-varying filtering. In this paper, a method to better carry out this process is presented and is based on the use of superresolution in the short-time Fourier transform (STFT) domain. This enhancement of the STFT is accomplished by nonparametric adaptive stationary extrapolations performed on each block of time samples. Superresolution also facilitates the definition of a component's support region in the time-frequency plane before it is edited. Synthesis is performed using the overlap add method that has been previously used to reconstruct a signal from its STFT, or a modified/edited version of it. A heuristic comparison is presented using a test signal using both: conventional and superresolution STFT-domain editing. Applications to radar imaging are also discussed.
A recent 1D, nonparametric procedure to extrapolate a signal is evaluated for resolution enhancement in inverse SAR imaging. This algorithm, denoted adaptive weighted norm extrapolation (AWNE), is based on iterative use of minimum weighted norm extrapolation to provide a stationary extension of the given data. Computing the discrete Fourier transform (DFT) spectrum of this signal completes the last step of this procedure when used as a spectrum estimator. In this paper the AWNE procedure is used in two directions to obtain range-Doppler images with improved resolution. We evaluate the results and compare them with those obtained with the conventional method based on the DFT. Using rectangularly sampled target data of noise corrupted point scatterers, we show that the AWNE approach produces accurate component locations and amplitudes as well as the expected higher resolution. Our examples show results for arrays of 63 by 63 samples extrapolated to 128 by 128 and 256 by 256. Next, we illustrate the application of AWNE to point scatterer data taken on a polar raster after it has undergone polar reformatting. The procedure is insensitive to the finite accuracy of the reformatting procedure needed to fit the samples into a rectangular raster. Finally, we illustrate the use of AWNE on an array of 64 by 64 data points to form the image of a Boeing 727 aircraft and compare results with those obtained via the conventional DFT processing.
In this paper, an evolutionary spectral estimator based on the application of Adaptive Weighted Norm Extrapolation (AWNE) is formulated and illustrated for analysis of nonstationary signals. The AWNE method produces a stationary extension of the data so that computing its Fourier transform yields a nonparametric, high-resolution spectrum estimate. The evolutionary formulation described here uses a time slice of the time-averaged Spectrogram to select the initial weight function (prior spectrum) used in AWNE for each block of data. This function strongly influences the final shape of the resulting spectrum. The resulting Short-Time AWNE (STAWNE) time-frequency representation yields improved frequency-domain resolution, preserves components which last longer than one time block, and is devoid of cross-terms. Comparison with short-time autoregressive spectral estimation yields improved consistency in the spectral energy levels as time varies. Finally, this sequential spectrum estimator is also illustrated for use in range-Doppler imaging of reflectivity surfaces having prominent scatterers by hybrid two-dimensional spectral estimation in-tandem with the discrete Fourier transform.
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