{"title":"Modelling optical pulse propagation in nonlinear media using wavelets","authors":"I. Pierce, L. Watkins","doi":"10.1109/TFSA.1996.547488","DOIUrl":"https://doi.org/10.1109/TFSA.1996.547488","url":null,"abstract":"A wavelet based model for propagation of optical pulses in nonlinear media is presented. We obtain an O(N) algorithm for linear propagation by replacing the wavelet-domain propagation operator by its Taylor series approximation. Nonlinear propagation is then achieved by adding the nonlinear term in mid-step in a method analogous to the split-step Fourier method. Using wavelets offers the advantage of O(N) computational complexity compared with O(N log N) for fast Fourier transform methods. Using a wavelet basis also leads naturally to the time-resolved spectrum of the signal. Another advantage is that the local properties of wavelets will allow locally adaptive algorithms to be implemented.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121323566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An operator theory approach to discrete time-frequency distributions","authors":"S. Narayanan, J. McLaughlin, L. Atlas, J. Droppo","doi":"10.1109/TFSA.1996.550107","DOIUrl":"https://doi.org/10.1109/TFSA.1996.550107","url":null,"abstract":"The theoretical link between a discrete-time sequence and its discrete-time/discrete-frequency representation has heretofore been established via a uniform sampling of their continuous-time counterparts. We provide a direct link between the two which we establish using the concepts of operator theory. We see that many similarities, but also some important differences, exist between the results of the continuous-time operator approach and our discrete one. The differences between the continuous distributions and discrete ones may not be the simple sampling relationship which has so often been assumed. Through basic matrix operations, discrete-time/discrete-frequency distributions can be generated using our operators, and we show that: (a) key properties like positivity are much easier to formulate and solve in the discrete case, and (b) while proper quadratic distributions are not possible using the Fourier transform, they do indeed exist for other transforms.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125694407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Snezana Maslakovic, I. Linscott, M. Oslick, J. Twicken
{"title":"Excising radio frequency interference using the discrete wavelet transform","authors":"Snezana Maslakovic, I. Linscott, M. Oslick, J. Twicken","doi":"10.1109/TFSA.1996.547485","DOIUrl":"https://doi.org/10.1109/TFSA.1996.547485","url":null,"abstract":"Radio frequency interference (RFI) excision methods have been developed using discrete wavelet transform (DWT) representations and wavelet selection based on optimizing entropy or energy by varying orthonormal wavelets and using a cost-based tree-search algorithm to compute the optimal sample shift. These methods have been applied to typical RFI waveforms obtained from Stanford's 150-foot parabolic antenna, and have succeeded in excluding the RFI while leaving background radio astronomy signals intact.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115491591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Smooth multiwavelets based on two scaling functions","authors":"P. Rieder, J. Nossek","doi":"10.1109/TFSA.1996.547475","DOIUrl":"https://doi.org/10.1109/TFSA.1996.547475","url":null,"abstract":"In this paper new multiwavelets based on several scaling functions are designed. The resulting wavelets exhibit the following properties: compact support, symmetry and orthogonality, arbitrary approximation order as well as good frequency resolution. The new bases are quite similar to the well known splines and also have close relationships to multirate filterbanks (multiwavelets based on one scaling function). The good performance of the new wavelets with respect to the smoothness and the frequency resolution is documented. A filterbank implementation is discussed.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122709613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Maximum-likelihood estimation of multiscale stochastic model parameters","authors":"K. C. Chou","doi":"10.1109/TFSA.1996.546675","DOIUrl":"https://doi.org/10.1109/TFSA.1996.546675","url":null,"abstract":"We consider the class of multiscale stochastic models developed by Chou, Willsky and Benveniste (see IEEE Trans. on Automatic Control, vol.39, no.3, 1994) and by Luettgen, Karl, Willsky and Tenney (see IEEE Trans. Signal Processing, vol.41, no.12, 1993) for signal and image modeling. These are Markov random field models on trees that describe signals in a scale-recursive way. In particular, they are state-space models with dynamics with respect to scale and have available fast algorithms for smoothing data. We present a maximum likelihood (ML) procedure for estimating the state-space parameters of these models from data. The procedure uses the expectation-maximization (EM) algorithm to iteratively solve for the ML estimates. Each iteration consists of (1) an expectation step that takes advantage of the fast smoother available for these multiscale models and (2) a maximization step that is also fast. We present an example of using this procedure to identify parameters based on imagery data and, subsequently, to perform multiscale target detection.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122189658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discrete frequency tracking in nonstationary signals using joint order statistics technique","authors":"A. Makarov","doi":"10.1109/TFSA.1996.550087","DOIUrl":"https://doi.org/10.1109/TFSA.1996.550087","url":null,"abstract":"In this communication we present a method for detecting periodicities which are superimposed on noisy and possibly discontinuous trends. This problem is encountered in practice whenever the baseline of the signal is susceptible of unpredictable variations. The discrete frequency estimate of periodicities superimposed on large trends is done by counting the extrema of the signal. The robustness of the method is provided by observing the variations of a pair of order statistics (a joint order statistic envelope) of the signal. The simultaneous change of sign of these variations correspond to extrema. We show how this yet unresolved problem can be, in extremis, reduced to a known and resolved problem of the removal of smooth trends.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129254718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal reduced-rank time-frequency/time-scale quadratic detectors","authors":"A. Sayeed, D.L. Jones","doi":"10.1109/TFSA.1996.547218","DOIUrl":"https://doi.org/10.1109/TFSA.1996.547218","url":null,"abstract":"Optimal detectors based on time-frequency/time-scale representations (TFRs/TSRs) admit a representation in terms of a bank of spectrograms/scalograms that yields a large class of detectors. These range from the conventional matched filter to the more complex higher-rank detectors offering a superior performance in a wider variety of detection situations. In this paper, we optimize this complexity versus performance tradeoff by characterizing TFR/TSR detectors that optimize performance (based on the deflection criterion) for any given fixed rank. We also characterize the gain in performance as a function of increasing complexity thereby facilitating a judicious tradeoff. Our experience with real data shows that, in many cases, relatively low-rank optimal detectors can provide most of the gain in performance relative to matched-filter processors.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130669747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multiresolution image reconstruction by wavelet decomposition","authors":"J. Núñez, X. Otazu","doi":"10.1109/TFSA.1996.547468","DOIUrl":"https://doi.org/10.1109/TFSA.1996.547468","url":null,"abstract":"We present a method of image reconstruction based on wavelet decomposition. The method seeks to overcome the problem of noise amplification during the image reconstruction process. We decompose the raw image to be reconstructed into several wavelet planes and a residual image, we reconstruct each one independently using an iterative maximum likelihood algorithm. To control the process, we stop the reconstruction of each one of the wavelet planes and the residual image at a different number of iterations. The stopping points are determined using the cross-validation method. The method has been applied to data from the non-refurbished Hubble Space Telescope.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114640722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A mutual information measure for feature selection with application to pulse classification","authors":"G. L. Barrows, J.C. Sciortino","doi":"10.1109/TFSA.1996.547460","DOIUrl":"https://doi.org/10.1109/TFSA.1996.547460","url":null,"abstract":"This paper presents a method of constructing a low dimensional representation of a pulse signal that preserves the information necessary to classify the pulse. A large set of \"atomic features\" are generated from dilations and shiftings of a family of one or more mother wavelet functions. Each atomic feature is used to generate a feature vector element by taking the inner product of the pulse with the atomic feature. The \"best\" feature vector elements are selected according to the mutual information between the pulse category and feature vector element values over all pulse realizations. The result is a low dimensional transformation that retains the information necessary to discriminate one category from another. This paper presents an algorithm for computing the above mutual information measure on a CNAPS, a 512 processor SIMD parallel computer.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"377 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116468427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Wavelet filter design for image compression","authors":"T. Strutz, E. Muller","doi":"10.1109/TFSA.1996.547466","DOIUrl":"https://doi.org/10.1109/TFSA.1996.547466","url":null,"abstract":"A new approach to wavelet filters optimized for image compression is proposed. Since the dyadic wavelet transform corresponds to convolutions of a signal with a high-pass and a low-pass filter in the time domain, it is useful to design the filters in the time domain aiming at a high energy compaction. The design technique introduced is based on a signal decomposition into suitable base functions. It is shown that this approach can lead to well-known wavelets, and furthermore the construction of new wavelet functions is possible.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126550110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}