HomeChair: S. Mallat, CMAP Ecole Polyechnique, France
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John G. Apostolopoulos, MIT (U.S.A.)
Jae S. Lim, MIT (U.S.A.)
Transform/subband representations form an important element of many signal processing algorithms and applications. Until recently, representations have typically been designed for signals with convenient supports, e.g. 2-D signals with rectangular supports. However, a number of applications require representations for signals with arbitrary (non-rectangular) regions of support. We present a novel algorithm for creating critically sampled perfect reconstruction wavelet representations for signals defined over arbitrary supports. The proposed algorithm selects a subset of vectors from a convenient superset basis which under appropriate conditions provides a basis over the given arbitrary support. The algorithm can be interpreted as solving a corresponding sampling problem.
ic985227.pdf (From Postscript)
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Roger L. Claypoole Jr, Rice University (U.S.A.)
Richard Baraniuk, Rice University (U.S.A.)
Robert D. Nowak, Michigan State University (U.S.A.)
This paper develops two new adaptive wavelet transforms based on the lifting scheme. The lifting construction exploits a spatial-domain, prediction-error interpretation of the wavelet transform and provides a powerful framework for designing customized transforms. We use the lifting construction to adaptively tune a wavelet transform to a desired signal by optimizing data-based prediction error criteria. The performances of the new transforms are compared to existing wavelet transforms, and applications to signal denoising are investigated.
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Brian M. Sadler, Army Research Laboratory (U.S.A.)
Ananthram Swami, Army Research Laboratory (U.S.A.)
We consider step detection and estimation using a multiscale wavelet analysis, based on the ability of a certain discrete wavelet transform (DWT) to characterize signal steps and edges. This DWT, developed by Mallat and Zhong, estimates the gradient at various smoothing levels without downsampling in time. As first proposed by Rosenfeld for edge sharpening, multiple scales are combined by forming the pointwise product across scales. We show that this approach is a non-linear whitening transformation, and characterize the non-Gaussian pdf of the output. Detection curves are shown forparameterized sigmoidal step change signals. Step location estimation performance is also shown, with comparison to the Cramer-Rao bound in additive white Gaussian noise.
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Maria A Trenas, University of Malaga (Spain)
Juan Lopez, University of Malaga (Spain)
Francisco Arguello, University of Santiago (Spain)
Emilio L Zapata, University of Malaga (Spain)
Real time image processing uses SIMD engines to accelerate the computation of algorithms as DCT, FFT or DWT.So, a good skewing scheme becomes essential for avoiding memory bank conflicts. In this paper a memory system is introduced for the efficient in-place computation of such transforms. It consists of $M=2^m$ memory modules, providing parallel access to M image points whose patterns are a row or a column, the interval in both cases being $2^l$, $l>=0$. The efficiency of our design is proved through the computation of the 2D-DWT.
ic981775.pdf (From Postscript) TOPMichael M Goodwin, University of California, Berkeley (U.S.A.)
The sinusoidal model has proven useful for representation and modification of speech and audio. One drawback, however, is that a sinusoidal signal model is typically derived using a fixed frame size, which corresponds to a rigid signal segmentation. For nonstationary signals, the resolution limitations that result from this rigidity lead to reconstruction artifacts. It is shown in this paper that such artifacts can be significantly reduced by using a signal-adaptive segmentation derived by a dynamic program. An atomic interpretation of the sinusoidal model is given; this perspective suggests that algorithms for adaptive segmentation can be viewed as methods for adapting the time scales of the constituent atoms so as to improve the model by employing appropriate time-frequency tradeoffs.
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Jerome Lebrun, Swiss Federal Institute of Technology, Lausanne (Switzerland)
Martin Vetterli, Swiss Federal Institute of Technology, Lausanne (Switzerland)
In this paper, we study the issue of regularity for multiwavelets. We generalize here the concept of balancing for higher degree discrete-time polynomial signals and link it to a very natural factorization of the lowpass refinement mask that is the counterpart of the well-known zeros at Pi condition for wavelets. This enables us to clarify the subtle relations between approximation power, smoothness and balancing order. Using these new results, we are also able to construct a family of orthogonal multiwavelets with symmetries and compact support that is indexed by the order of balancing. More details (filters coefficients, drawings of the whole family, frequency responses, etc.) can be obtained on the [WEB] at: http://lcavwww.epfl.ch/~lebrun.
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James M Lewis, Rice University (U.S.A.)
C. Sidney Burrus, Rice University (U.S.A.)
We describe a generalized scale-redundant wavelet transform which approximates a dense sampling of the continuous wavelet transform (CWT) in both time and scale. The dyadic scaling requirement of the usual wavelet transform is relaxed in favor of an approximate scaling relationship which in the case of a Gaussian scaling function is known to be asymptotically exact and irrational. This scheme yields an arbitrarily dense sampling of the scale axis in the limit. Similar behavior is observed for other scaling functions with no explicit analytic form. We investigate characteristics of the family of Lagrange interpolating filters (related to the Daubechies family of compactly-supported orthonormal wavelets), and finally present applications of the transform to denoising and edge detection.
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Mitchell Oslick, Stanford University (U.S.A.)
Ivan R. Linscott, Stanford University (U.S.A.)
Snezana Maslakovic, Stanford University (U.S.A.)
Joseph D. Twicken, Stanford University (U.S.A.)
Biorthogonal bases of compactly-supported wavelets are characterized by the FIR perfect-reconstruction filterbanks to which they correspond. In this paper we develop explicit representations of all such filterbanks, allowing us to generate every possible biorthogonal compactly-supported wavelet basis. For these filterbanks, the product of the two lowpass filters must have N zeros at z = -1, where N is two or more. There are N+1 minimal-length filterbanks for each N. The filterbanks associated with standard orthogonal and symmetric biorthogonal wavelet bases are found as a special case by using appropriate factorizations of symmetric product filters with even N; other filterbanks lead to novel biorthogonal bases.
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C. Sidney Burrus, Rice University (U.S.A.)
Jan E. Odegard, Rice University (U.S.A.)
The Coifman wavelets created by Daubechies have more zero moments than imposed by specifications. This results in systems with approximately equal numbers of zero scaling function and wavelet moments and gives a partitioning of the systems into three well defined classes. The nonunique solutions are more complex than for Daubechies wavelets.
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Tai-Chiu Hsung, The Hong Kong Polytechnic University (Hong Kong)
Daniel Pak-Kong Lun, The Hong Kong Polytechnic University (Hong Kong)
Blocking effect is considered as the most disturbing artifact of JPEG decoded images. Many researchers have suggested various methods to tackle this problem. Recently, the wavelet transform modulus maxima (WTMM) approach was proposed and gives a significant improvement over the previous methods in terms of signal-to-noise ratio and visual quality.However, the WTMM deblocking algorithm is an iterative algorithm that requires a long computation time to reconstruct the processed WTMM to obtain the deblocked image. In this paper, a new wavelet based algorithm for JPEG image deblocking is proposed. The new algorithm is based on the idea that, besides using the WTMM, the singularity of an image can also be detected by computing the sums of the wavelet coefficients inside the so-called ""directional cone of influence"" in different scales of the image. The new algorithm has the advantage as the WTMM approach that it can effectively identify the edge and the smooth regions of an image irrespective the discontinuities introduced by the blocking effect. It improves over the WTMM approach in that only a simple inverse wavelet transform is required to reconstruct the processed wavelet coefficients to obtain the deblocked image. As the WTMM approach, the new algorithm gives consistent and significant improvement over the previous methods for JPEG image deblocking.
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