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Optimal wavelet representation and of signals and the wavelet sampling theorem
 IEEE Trans. Circuits Syst., II: Analog Digit. Signal Process
, 1994
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Theory and Applications of the ShiftInvariant, TimeVarying and Undecimated Wavelet Transforms
, 1995
"... In this thesis, we generalize the classical discrete wavelet transform, and construct wavelet transforms that are shiftinvariant, timevarying, undecimated, and signal dependent. The result is a set of powerful and efficient algorithms suitable for a wide variety of signal processing tasks, e.g., d ..."
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Cited by 20 (3 self)
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In this thesis, we generalize the classical discrete wavelet transform, and construct wavelet transforms that are shiftinvariant, timevarying, undecimated, and signal dependent. The result is a set of powerful and efficient algorithms suitable for a wide variety of signal processing tasks, e.g., data compression, signal analysis, noise reduction, statistical estimation, and detection. These algorithms are comparable and often superior to traditional methods. In this sense, we put wavelets in action.
Enhancement of Decompressed Images at Low Bit Rates
 Rice University
, 1994
"... Transform coding at low bit rates introduces artifacts associated with the basis functions of the transform. For example, decompressed images based on the DCT (discrete cosine transform)  like JPEG 16  exhibit blocking artifacts at low bit rates. This paper proposes a postprocessing scheme to e ..."
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Cited by 8 (5 self)
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Transform coding at low bit rates introduces artifacts associated with the basis functions of the transform. For example, decompressed images based on the DCT (discrete cosine transform)  like JPEG 16  exhibit blocking artifacts at low bit rates. This paper proposes a postprocessing scheme to enhance decompressed images that is potentially applicable in several situations. In particular, the method works remarkably well in "deblocking" of DCT compressed images. The method is nonlinear, computationally efficient, and spatially adaptive  and has the distinct feature that it removes artifacts while yet retaining sharp features in the images. An important implication of this result is that images coded using the JPEG standard can be efficiently postprocessed to give significantly improved visual quality in the images. Keywords: image enhancement, wavelet shrinkage, jpeg, image restoration, image compression 1 INTRODUCTION Effective compression of still images such as the JPEG sta...
On The Moments Of The Scaling Function
, 1992
"... This paper derives relationships between the moments of the scaling function /0(t) associated with multiplicity M , Kregular, compactly supported, orthonormal wavelet bases [6, 5], that are extensions of the multiplicity 2, Kregular orthonormal wavelet bases constructed by Daubechies [2]. One suc ..."
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Cited by 7 (1 self)
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This paper derives relationships between the moments of the scaling function /0(t) associated with multiplicity M , Kregular, compactly supported, orthonormal wavelet bases [6, 5], that are extensions of the multiplicity 2, Kregular orthonormal wavelet bases constructed by Daubechies [2]. One such relationship is that the square of the first moment of the scaling function (/0(t)) is equal to its second moment. This relationship is used to show that uniform sample values of a function provides a third order approximation of its scaling function expansion coefficients. For the special case of M = 2, the results in this paper have been reported earlier [3]. 1. INTRODUCTION In this paper we derive relationships between the moments of the scaling function /0(t) associated with the compactly supported, multiplicity M , K regular, orthonormal wavelet bases. In particular, we show that the square of the first moment of /0 is the second moment of /0 . Hence samples of a function accurately ...
Optimal Wavelets for Signal Decomposition and the Existence of ScaleLimited Signals
 In Proc. Int. Conf. Acoust., Speech, Signal Processing
, 1992
"... Wavelet methods give a flexible alternative to Fourier methods in nonstationary signal analysis. The concept of bandlimitedness plays a fundamental role in Fourier analysis. Since wavelet theory replaces frequency with scale, a natural question is whether there exists a useful concept of scalel ..."
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Cited by 3 (1 self)
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Wavelet methods give a flexible alternative to Fourier methods in nonstationary signal analysis. The concept of bandlimitedness plays a fundamental role in Fourier analysis. Since wavelet theory replaces frequency with scale, a natural question is whether there exists a useful concept of scalelimitedness. Obvious definitions of scalelimitedness are too restrictive, in that there would be few or no useful scalelimited signals. This paper introduces a viable definition for scalelimited signals, and shows that the class is rich enough to include bandlimited signals, and impulse trains, among others. Moreover, for a wide choice of criteria, we show how to design the optimal wavelet for representing a given signal, and how to design robust wavelets that optimally represent certain classes of signals. Also Technical Report Rice University, CML TR9107 1. INTRODUCTION The recognition and existence of band limited signals plays a fundamental role in sampling theory and Fourier analys...
Dimensional Signal Analysis of Multichannel Spectrometric Imagery
 Proceedings of EARSeL '95
, 1996
"... Hyperspectral, multispectral and multitemporal satellite images are considered as 3D signals and processed using 3D signal techniques. The third dimension is given by the spectral/temporal channels and the idea to perform a 3D processing is an attempt to take advantage of the correlation existing be ..."
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Hyperspectral, multispectral and multitemporal satellite images are considered as 3D signals and processed using 3D signal techniques. The third dimension is given by the spectral/temporal channels and the idea to perform a 3D processing is an attempt to take advantage of the correlation existing between these channels in order to achieve higher data compression rates. Two methods are investigated and compared: a 3D linear predictor based on a low order Markov model and a 3D wavelet decomposition procedure. Although the compression rate depends highly on the structure of the data, the 3D algorithms perform always better than the 2D ones. This justifies the use of 3D signal processing techniques in remote sensing applications involving a large number of correlated spectral or temporal channels.
Factorization Approach To Unitary TimeVarying Filter Banks
, 1992
"... A complete factorization of all optimal (in terms of quick transition) timevarying FIR unitary filter bank tree topologies is obtained. This has applications in adaptive subband coding, tiling of the timefrequency plane and the construction of orthonormal wavelet bases for the halfline and interv ..."
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A complete factorization of all optimal (in terms of quick transition) timevarying FIR unitary filter bank tree topologies is obtained. This has applications in adaptive subband coding, tiling of the timefrequency plane and the construction of orthonormal wavelet bases for the halfline and interval [9, 8, 13, 2]. A simple efficient implementation algorithm also comes with the factorization ensuring that even the most complex tree topology can be adapted with minimal overhead. Explicit formulas for entry/exit filters are given for arbitrary tree transitions. The results are independent of the number of channels and the length of the filters (as long as they are FIR), implying that some of the efficiency reasons for considering only binary timevarying trees is not valid any more. Timevarying wavelet bases (different bases for different segments of the real line) are also constructed. Contact Address: Ramesh A. Gopinath Department of EE, A235 Rice University, Houston, TX77251 Phone (...