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32
Orthonormal ShiftInvariant Wavelet Packet Decomposition and Representation
 Signal Processing
, 1995
"... In this work, a shifted wavelet packet (SWP) library, containing all the time shifted wavelet packet bases, is defined. A corresponding shiftinvariant wavelet packet decomposition (SIWPD) search algorithm for a "best basis" is introduced. The search algorithm is representable by a binar ..."
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Cited by 32 (8 self)
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In this work, a shifted wavelet packet (SWP) library, containing all the time shifted wavelet packet bases, is defined. A corresponding shiftinvariant wavelet packet decomposition (SIWPD) search algorithm for a "best basis" is introduced. The search algorithm is representable by a binary tree, in which a node symbolizes an appropriate subspace of the original signal. We prove that the resultant "best basis" is orthonormal and the associated expansion, characterized by the lowest information cost, is shiftinvariant. The shiftinvariance stems from an additional degree of freedom, generated at the decomposition stage and incorporated into the search algorithm. The added dimension is a relative shift between a given parentnode and its respective childrennodes. We prove that for any subspace it suffices to consider one of two alternative decompositions, made feasible by the SWP library. These decompositions correspond to a zero shift and a 2  relative shift where denotes the resolution level.
Bilinear Signal Synthesis in Array Processing
 in Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing
, 2001
"... Multiple source signals impinging on an antenna array can be separated by timefrequency synthesis techniques. Averaging of the timefrequency distributions of the data across the array permits the spatial signatures of sources to play a fundamental role in improving the synthesis performance. This ..."
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Cited by 17 (16 self)
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Multiple source signals impinging on an antenna array can be separated by timefrequency synthesis techniques. Averaging of the timefrequency distributions of the data across the array permits the spatial signatures of sources to play a fundamental role in improving the synthesis performance. This improvement is achieved independent of the temporal characteristics of the source signals and without causing any smearing of the signal terms. Unlike the recently devised blind source separation methods using spatial timefrequency distributions, the proposed methoddoes not requirewhitening
Compressive sensing in nonstationary array processing using bilinear transforms
 in Proc. IEEE
, 2012
"... Compressive sensing (CS) has successfully been applied to reconstruct sparse signals and images from few observations. For multicomponent nonstationary signals characterized by instantaneous frequency laws, the sparsity exhibits itself in the timefrequency domain as well as the ambiguity domain ..."
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Cited by 11 (10 self)
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Compressive sensing (CS) has successfully been applied to reconstruct sparse signals and images from few observations. For multicomponent nonstationary signals characterized by instantaneous frequency laws, the sparsity exhibits itself in the timefrequency domain as well as the ambiguity domain. In this paper, we examine CS in the context of nonstationary array processing. We show that the spatial averaging of the ambiguity function across the array improves the CS performance by reducing both noise and crossterms. The corresponding timefrequency distribution which is reconstructed through L1 minimizations yields significant improvement in timefrequency signature localizations and characterizations. 1.
Timefrequency signature reconstruction from random observations using multiple measurement vectors
 in Proc. IEEE ICASSP
, 2014
"... A new approach for sparse nonstationary signal reconstruction based on multiple windows is introduced. Signals which are localizable in the timefrequency (TF) domain give rise to sparsity in the same domain. When combined, sparse reconstructions, applied to randomly sampled data and corresponding ..."
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Cited by 10 (10 self)
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A new approach for sparse nonstationary signal reconstruction based on multiple windows is introduced. Signals which are localizable in the timefrequency (TF) domain give rise to sparsity in the same domain. When combined, sparse reconstructions, applied to randomly sampled data and corresponding to different selected windows, provide enhanced TF signature estimation. Among possible orthogonal windows, we consider those which characterize the eigendecomposition of reducedinterference quadratic timefrequency distribution kernels. The highly overlapping TF support of the windows ’ fulldata spectrograms inspires the use of the multiple measurement vectors, in lieu of individual windowed signal recovery. It is shown that the proposed approach outperforms other reconstruction methods when only a single window is applied and is superior to reduced interference timefrequency distributions of random observations. Index Terms — Timefrequency distribution, multiple measurement vector, compressive sensing, random sampling 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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Cited by 9 (1 self)
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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.
Spatial polarimetric timefrequency distributions for directionofarrival estimations
 IEEE Trans. Signal Processing
, 2006
"... Timefrequency distributions (TFDs) have evolved to be a powerful technique for nonstationary signal analysis and synthesis. With the use of a multisensor array, spatial timefrequency distributions (STFDs) have been developed and successfully applied to highresolution directionofarrival (DOA) e ..."
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Cited by 8 (4 self)
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Timefrequency distributions (TFDs) have evolved to be a powerful technique for nonstationary signal analysis and synthesis. With the use of a multisensor array, spatial timefrequency distributions (STFDs) have been developed and successfully applied to highresolution directionofarrival (DOA) estimation and blind recovery of the source waveforms. In this paper, the polarimetric dimension is introduced to the STFDs resulting in the spatial polarimetric timefrequency distributions (SPTFDs) as a platform for the processing of nonstationary polarized signals. In the SPTFD platform, polarized signals are decomposed (projected) into two orthogonal polarization components, such as horizontal and vertical, and later processed in a manner where their polarization characteristics are exploited. This empowers the STFDs with additional degrees of freedom and improves the robustness of the signal and noise subspaces, and therefore, serving to enhance DOA estimation, signal recovery, and source separation performance. To demonstrate the advantages of the SPTFDs, the polarimetric timefrequency MUSIC (PTFMUSIC) method for DOA estimation is proposed based on the SPTFD platform and is shown to outperform the timefrequency, polarimetric, and conventional MUSIC methods.
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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Cited by 7 (0 self)
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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.
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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Cited by 4 (1 self)
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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.
Linear and synchrosqueezed timefrequency representations revisited
 Digital Signal Processing, arXiv:1310.7215v2 [math.NA
, 2013
"... Having reviewed the aspects of the linear and synchrosqueezed timefrequency representations (TFRs) needed for their understanding and correct use in Part I of this review, we now consider three more subtle issues that are nonetheless of crucial importance for effective application of these methods ..."
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Cited by 4 (2 self)
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Having reviewed the aspects of the linear and synchrosqueezed timefrequency representations (TFRs) needed for their understanding and correct use in Part I of this review, we now consider three more subtle issues that are nonetheless of crucial importance for effective application of these methods. (i) What effect do the window/wavelet parameters have on the resultant TFR, and how can they most appropriately be chosen? (ii) What are the errors inherent in the two reconstruction methods (direct and ridge) and which of them is the better? (iii) What are the advantages and drawbacks associated with synchrosqueezing? To answer these questions, we perform a detailed numerical and theoretical study of the TFRs under consideration. We consider the relevant estimates in the presence of the complications that arise in practical applications including interference between components, amplitude modulation, frequency modulation, and noise. Taken together, the results provide an indepth understanding of the issues in question.