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12
TranslationInvariant Denoising Using the Minimum Description Length Criterion
, 1999
"... A translationinvariant denoising method based on the minimum description length (MDL) criterion and treestructured bestbasis algorithms is presented. A collection of signal models is generated using an extended library of orthonormal waveletpacket bases, and an additive cost function, approximate ..."
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Cited by 4 (2 self)
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A translationinvariant denoising method based on the minimum description length (MDL) criterion and treestructured bestbasis algorithms is presented. A collection of signal models is generated using an extended library of orthonormal waveletpacket bases, and an additive cost function, approximately representing the MDL principle, is derived. We show that the minimum description length of the noisy observed data is achieved by utilizing the shiftinvarient wavelet packet decomposition (SIWPD) and thresholding the resulting coefficients. This approach is extendable to local trigonometric decompositions, and corresponding procedures to optimize either the library of bases or the filter banks used at each node of the expansiontree are described. The signal estimator is efficiently combined with a modified Wigner distribution, yielding robust timefrequency representations, characterized by high resolution and suppressed interferenceterms. The proposed method is compared to alternative existing methods, and its superiority is demonstrated by synthetic and real data examples.
The evolution of modern texture processing
 Elektrik
, 1997
"... Abstract { This paper studies the evolution of image texture processing techniques over the last 20 years. Although texture is a fundamental attribute of images that has been shown to play an important role in human visual perception, the quanti cation and characterization of texture is di cult. Ear ..."
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Abstract { This paper studies the evolution of image texture processing techniques over the last 20 years. Although texture is a fundamental attribute of images that has been shown to play an important role in human visual perception, the quanti cation and characterization of texture is di cult. Early texture processing techniques described texture deterministically or statistically in terms of repeated graylevel patterns and the structure of the spatial placement of these patterns. Gray level cooccurrence matrices were among the most successful such methods. Modern texture processing techniques tend to characterize texture in terms of spatiospectrally localized coherent amplitude, frequency, and phase modulations. This paper argues that evolution of the modern methods from the early methods can be directly linked to advances in the understanding of mammalian biological visual function that occurred in the elds of psychophysics and physiology, and furthermore that the most successful modern methods have evolved to emulate biological vision systems. Evolution of modern texture processing methods is examined, and several of the most successful new techniques such as the multidimensional TeagerKaiser operator and AMFM modeling techniques are described in some detail. The use of computed dominant modulations to perform e ective texture segmentation is demonstrated for the rst time.
WideAngle ISAR Passive Imaging Using Smoothed Pseudo WignerVille Distribution
 IEEE Radar Conference Proceedings
, 2001
"... reflected TV signals. UHFband TSAR imaging requires wideangle data to produce good crossrange resolution. We show that direct Fourier reconstruction (DFR) causes degradation of the reconstructed image due to aspectdependent scattering. We find that a Smoothed Pseudo WignerVille distribution (SP ..."
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reflected TV signals. UHFband TSAR imaging requires wideangle data to produce good crossrange resolution. We show that direct Fourier reconstruction (DFR) causes degradation of the reconstructed image due to aspectdependent scattering. We find that a Smoothed Pseudo WignerVille distribution (SPWVD) applied in the crossrange direction in place of the Fourier transform can generate a sequence of images, which shows the target reflectivity as a function of aspect angle. Compared to DFR results, these images have higher crossrange resolution. A final image can be synthesized from these images and used for target recogni tion. XPATCH is used to simulate monostatic data from an aircraft. The proposed SPWVDbased imaging method produces a useful image of the aircraft from this data.
Adaptive Suppression of Wigner InterferenceTerms Using ShiftInvariant Wavelet Packet Decompositions
 Tech. Rep., CC PUB No. 245, Dept. of Elect. Eng., Technion  IIT
, 1999
"... The Wigner distribution (WD) possesses a number of desirable mathematical properties relevant to timefrequency analysis. However, the presence of interference terms renders the WD of multicomponent signals extremely difficult to interpret. In this work, we propose adaptive suppression of interferen ..."
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Cited by 3 (2 self)
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The Wigner distribution (WD) possesses a number of desirable mathematical properties relevant to timefrequency analysis. However, the presence of interference terms renders the WD of multicomponent signals extremely difficult to interpret. In this work, we propose adaptive suppression of interference terms using the shiftinvariant wavelet packet decomposition. A prescribed signal is expanded on its best basis and transformed into the Wigner domain. Subsequently, the interference terms are eliminated by adaptively thresholding the crossWD of interactive basis functions, according to their amplitudes and distance in an idealized timefrequency plane. We define a distance measure that weighs the Euclidean distance with the local distribution of the signal. The amplitude and distance thresholds control the crossterm interference, the useful properties of the distribution, and the computational complexity. The properties of the resultant modified igner distribution (MWD) are investigated, and its performance in eliminating interference terms, while still retaining highenergy resolution, is compared with that of other existing approaches. It is shown that the proposed MWD is directly applicable to resolving multicomponent signals. Each component is determined as a partial sum of basis functions over a certain equivalence class in the timefrequency plane.
Multistatic Passive Radar Imaging Using The Smoothed Pseudo WignerVille Distribution
 in Proc. IEEE Intl. Conf. on Image Processing
, 2001
"... We investigate passive radar imaging of aircraft using reflected TV signals. We apply a Smoothed Pseudo WignerVille Distribution (SPWVD)based SAR imaging algorithm to two different scenarios. In the first simulation, multistatic VHFband dataset generated by Fast Illinois Solver Code (FISC) is used ..."
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We investigate passive radar imaging of aircraft using reflected TV signals. We apply a Smoothed Pseudo WignerVille Distribution (SPWVD)based SAR imaging algorithm to two different scenarios. In the first simulation, multistatic VHFband dataset generated by Fast Illinois Solver Code (FISC) is used. In the second simulation, a more realistic simulated passive radar dataset is used. A set of instantaneous images are produced by our algorithm, which have higher resolution and show more detail and features of the aircraft than can be obtained by Direct Fourier Reconstruction (DFR). The set of images provides visually more information about the target and helps to estimate its shape and features. This study suggests that the SPWVDbased imaging might be useful in passive radar imaging and target classification. 1.
Fetal Heart Rate Variability Extraction by Frequency Tracking
 in Proceedings of ICA’01
, 2001
"... In this work, we propose an algorithm to extract the fetal heart rate variability from an ECG measured from the mother abdomen. The algorithm consists of two methods: a separation algorithm based on secondorder statistics that extracts the desired signal in one shot through the data, and a hearth i ..."
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In this work, we propose an algorithm to extract the fetal heart rate variability from an ECG measured from the mother abdomen. The algorithm consists of two methods: a separation algorithm based on secondorder statistics that extracts the desired signal in one shot through the data, and a hearth instantaneous frequency (HIF) estimator. The HIF algorithm is used to extract the mother heart rate which serves as reference to extract the fetal heart rate. We carried out simulations where the signals overlap in frequency and time, and showed that the it worked efficiently.
ShiftInvariant Adaptive Wavelet Decompositions And Applications
 Dissertation, Technion  Israel Institute of Technology
, 1998
"... List of Symbols and Abbreviations 4 1 ..."
Slepian Functions and Their Use in Signal Estimation and Spectral Analysis
, 909
"... It is a wellknown fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access t ..."
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It is a wellknown fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are “spatiospectrally” concentrated, i.e. “localized ” in both domains at the same time. Here, we give a theoretical overview of one particular approach to this “concentration ” problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.
WIGNERVILLE SPECTRUM ESTIMATION
"... The high noise sensitivity of the Wigner distribution makes smoothing a necessity for producing readable timefrequency images of noise corrupted signals. Since linear smoothing suppresses noise at the expense of considerable smearing of the signal components, we explore two nonlinear denoising tec ..."
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The high noise sensitivity of the Wigner distribution makes smoothing a necessity for producing readable timefrequency images of noise corrupted signals. Since linear smoothing suppresses noise at the expense of considerable smearing of the signal components, we explore two nonlinear denoising techniques based on softthresholding in an orthonormal basis representation. Softthresholding provides considerable noise reduction without greatly impairing the time frequency resolution of the denoised distribution. 1.
Positive timefrequency distributions via maximum entropy deconvolution of the evolutionary spectrum
 IEEE Proc. ICASSP’93
"... The relationship between Priestley's definition of the evolutionary spectrum (ES) and the CohenPosch class of positive timefrequency energy densities (TFDs) is explored, and a synthesis method is presented. As defined by Priestley, the ES is not a member of the CohenPosch class of TFDs. However, ..."
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The relationship between Priestley's definition of the evolutionary spectrum (ES) and the CohenPosch class of positive timefrequency energy densities (TFDs) is explored, and a synthesis method is presented. As defined by Priestley, the ES is not a member of the CohenPosch class of TFDs. However, it is shown that by choosing a unitenergy normalization for the envelope function of Priestley's formulation, the "energetic" ES thus obtained is a member of the CohenPosch class of TFDs; this normalization differs from that chosen by Priestley. A method is then presented to obtain an estimate of the energetic ES. This method employs maximum entropy deconvolution of the spectrogram, which is itself a blurred version of the ES. Because the energetic ES is everywhere nonnegative and yields the correct marginal densities, it is a legitimate, joint timefrequency energy density of the signal, unlike the Wigner and other bilinear distributions that go negative. Introduction Signals with time...