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34
Complete discrete 2D Gabor transforms by neural networks for image analysis and compression
, 1988
"... AbstractA threelayered neural network is described for transforming twodimensional discrete signals into generalized nonorthogonal 2D “Gabor ” representations for image analysis, segmentation, and compression. These transforms are conjoint spatiahpectral representations [lo], [15], which provide ..."
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Cited by 475 (8 self)
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AbstractA threelayered neural network is described for transforming twodimensional discrete signals into generalized nonorthogonal 2D “Gabor ” representations for image analysis, segmentation, and compression. These transforms are conjoint spatiahpectral representations [lo], [15], which provide a complete image description in terms of locally windowed 2D spectral coordinates embedded within global 2D spatial coordinates. Because intrinsic redundancies within images are extracted, the resulting image codes can be very compact. However, these conjoint transforms are inherently difficult to compute because t e elementary expansion functions are not orthogonal. One orthogonking approach developed for 1D signals by Bastiaans [SI, based on biorthonormal expansions, is restricted by constraints on the conjoint sampling rates and invariance of the windowing function, as well as by the fact that the auxiliary orthogonalizing functions are nonlocal infinite series. In the present “neural network ” approach, based
Multiresolution Support Applied to Image Filtering and Restoration
, 1995
"... The notion of a multiresolution support is introduced. This is a sequence of boolean images, related to significant pixels at each of a number of resolution levels. The multiresolution support is then used for noise suppression, in the context of image filtering, or iterative image restoration. A ..."
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Cited by 46 (21 self)
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The notion of a multiresolution support is introduced. This is a sequence of boolean images, related to significant pixels at each of a number of resolution levels. The multiresolution support is then used for noise suppression, in the context of image filtering, or iterative image restoration. Algorithmic details, and a range of practical examples, illustrate this approach.
Fast GaborLike Windowed Fourier and Continuous Wavelet Transforms
 IEEE Signal Processing Letters
, 1994
"... Fast algorithms for the evaluation of running windowed Fourier and continuous wavelet transforms are presented. The analysis functions approximate complexmodulated Gaussians as closely as desired and may be optimally localized in time and frequency. The Gabor filtering is performed indirectly by co ..."
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Cited by 16 (4 self)
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Fast algorithms for the evaluation of running windowed Fourier and continuous wavelet transforms are presented. The analysis functions approximate complexmodulated Gaussians as closely as desired and may be optimally localized in time and frequency. The Gabor filtering is performed indirectly by convulving a premodulated signal with a Gaussianlike window and demodulating the output. The window functions are either Bsplines dilated by an integer factor m or quasi.Gaussians of arbitrary size generated from the ,fold convolution of a symmetrical exponential. Both approaches result in a recursive implementation with a complexity independent of the window size (O(N)).
Overcoming the Curse of Dimensionality in Clustering by means of the Wavelet Transform
 The Computer Journal
, 2000
"... We use a redundant wavelet transform analysis to detect clusters in highdimensional data spaces. We overcome Bellman's \curse of dimensionality" in such problems by (i) using some canonical ordering of observation and variable (document and term) dimensions in our data, (ii) applying a ..."
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Cited by 14 (5 self)
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We use a redundant wavelet transform analysis to detect clusters in highdimensional data spaces. We overcome Bellman's \curse of dimensionality" in such problems by (i) using some canonical ordering of observation and variable (document and term) dimensions in our data, (ii) applying a wavelet transform to such canonically ordered data, (iii) modeling the noise in wavelet space, (iv) dening signicant component parts of the data as opposed to insignicant or noisy component parts, and (v) reading o the resultant clusters. The overall complexity of this innovative approach is linear in the data dimensionality. We describe a number of examples and test cases, including the clustering of highdimensional hypertext data. 1 Introduction Bellman's (1961) [1] \curse of dimensionality" refers to the exponential growth of hypervolume as a function of dimensionality. All problems become tougher as the dimensionality increases. Nowhere is this more evident than in problems related to ...
Selfinvertible 2D LogGabor Wavelets
, 2007
"... Orthogonal and biorthogonal wavelets became very popular image processing tools but exhibit major drawbacks, namely a poor resolution in orientation and the lack of translation invariance due to aliasing between subbands. Alternative multiresolution transforms which specifically solve these drawback ..."
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Cited by 12 (1 self)
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Orthogonal and biorthogonal wavelets became very popular image processing tools but exhibit major drawbacks, namely a poor resolution in orientation and the lack of translation invariance due to aliasing between subbands. Alternative multiresolution transforms which specifically solve these drawbacks have been proposed. These transforms are generally overcomplete and consequently offer large degrees of freedom in their design. At the same time their optimization gets a challenging task. We propose here the construction of logGabor wavelet transforms which allow exact reconstruction and strengthen the excellent mathematical properties of the Gabor filters. Two major improvements on the previous Gabor wavelet schemes are proposed: first the highest frequency bands are covered by narrowly localized oriented filters. Secondly, the set of filters cover uniformly the Fourier domain including the highest and lowest frequencies and thus exact reconstruction is achieved using the same filters in both the direct and the inverse transforms (which means that the transform is selfinvertible). The present transform not only achieves important mathematical properties, it also follows as much as possible the knowledge on the receptive field properties of the simple cells of the Primary Visual Cortex (V1) and on the statistics of natural images. Compared to the state of the art, the logGabor wavelets show excellent ability to segregate the image information (e.g. the contrast edges) from spatially incoherent Gaussian noise by hard thresholding, and then to represent image features through a reduced set of
Historic climate variability of wetness in east China (9601992): a w avelet analysis
 1nternational Journal ofClimatology
, 1997
"... Temporal and spatial climate variability in East China is analysed for the last 1033 years (AD 960–1992) based on historic annual grades of wetness for six regions in East China. This data set is subjected to a ‘Mexican hat ’ wavelet transform for displaying variations of different frequencies at pa ..."
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Cited by 5 (0 self)
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Temporal and spatial climate variability in East China is analysed for the last 1033 years (AD 960–1992) based on historic annual grades of wetness for six regions in East China. This data set is subjected to a ‘Mexican hat ’ wavelet transform for displaying variations of different frequencies at particular time points, persistent anomalies, and abrupt changes between them. The following results are noted: the persistent dry stage 1120–1220 and wet stage 1280–1390 in the coastal regions are the outstanding features during the last 1033 years. For all regions an almost synchronous change occurs around 1890 from a weaker wet phase to a weaker dry phase; climatic variations on longer timescales cover larger areas. On shorter timescales, synchronous fluctuations are observed in fewer years than longer timescale variability. # 1997 by the Royal Meteorological
Pattern Clustering based on Noise Modeling in Wavelet Space
, 1997
"... We describe an effective approach to object or feature detection in point patterns via noise modeling. This is based on use of a redundant or nonpyramidal wavelet transform. Noise modeling is based on a Poisson process. We illustrate this new method with a range of examples. We use the close rel ..."
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Cited by 4 (4 self)
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We describe an effective approach to object or feature detection in point patterns via noise modeling. This is based on use of a redundant or nonpyramidal wavelet transform. Noise modeling is based on a Poisson process. We illustrate this new method with a range of examples. We use the close relationship between image (pixelated) and point representations to achieve the result of a clustering method with constanttime computational cost. Keywords: Cluster analysis, point pattern, `a trous wavelet transform, noise modeling, Poisson distribution, minefield detection. 1 Introduction Point pattern clustering has constituted one of major strands in cluster analysis. We will briefly describe some of this work, in order to motivate the need for (i) a multiscale approach which 1 is computationally very efficient, and (ii) a direct treatment of noise and clutter which leads to improved cluster detection. In the following the first few categories of work proceed in the direction of a m...
WAVELETBASED IDENTIFICATION OF LINEAR DISCRETETIME SYSTEMS
"... Discretetime linear timevarying systems are modeled by discretetime wavelets. System identification using the output error method is studied. The output of the unknown system is in general corrupted by noise. The minimum mean square error, minimum cumulative mean square error and least squares ..."
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Cited by 3 (0 self)
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Discretetime linear timevarying systems are modeled by discretetime wavelets. System identification using the output error method is studied. The output of the unknown system is in general corrupted by noise. The minimum mean square error, minimum cumulative mean square error and least squares are considered. The optimal system model parameters are found. Conditions are derived that provide consistency to the optimal parameters obtained by the least squares approach. It is shown that due to the good timefrequency localization of wavelets, parameter estimates are robust to narrowband noise and/or impulse noise.
On the synthesis of regular VLSI architectures for the 1D discrete wavelet transform
 PROCEEDINGS OF SPIE CONF. ON MATHEMATICAL IMAGING: WAVELET APPLICATIONS IN SIGNAL AND IMAGE PROCESSING II
, 1994
"... A methodology for synthesizing parallel computational structures has been applied to the Discrete Wavelet Transform algorithm. It is based on linear spacetime mapping with constraint driven localization. The data dependence analysis, localization of global variables, and spacetime mapping is prese ..."
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Cited by 3 (1 self)
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A methodology for synthesizing parallel computational structures has been applied to the Discrete Wavelet Transform algorithm. It is based on linear spacetime mapping with constraint driven localization. The data dependence analysis, localization of global variables, and spacetime mapping is presented, as well as one realization of a 3octave systolic array. The DWT algorithm may not be described by a set of Uniform or Affine Recurrence Equations (UREs, AREs), thus it may not be efficiently mapped onto a regular array. However it is still possible to map the DWT algorithm to a systolic array with local communication links by using first a nonlinear index space transformation. The array derived here has latency of 3M=2, where M is the input sequence length, and similar area requirements as solutions proposed elsewhere. In the general case of an arbitrary number of octaves, linear spacetime mapping leads to inefficient arrays with long latency due to problems associated with multipro...