Seismic data and their complexity still challenge signal processing algorithms in several applications. The advent
of wavelet transforms has allowed improvements in tackling denoising problems. We propose here coherent noise
filtering in seismic data with the dual-tree M-band wavelet transform. They offer the possibility to decompose
data locally with improved multiscale directions and frequency bands. Denoising is performed in a deterministic
fashion in the directional subbands, depending of the coherent noise properties. Preliminary results show that
they consistently better preserve seismic signal of interest embedded in highly energetic directional noises than
discrete critically sampled and redundant separable wavelet transforms.
The Short Term Fourier Transform (STFT) is a classical linear time-frequency (T-F) representation. Despites
its relative simplicity, it has become a standard tool for the analysis of non-stationary signals. Since it provides a
redundant representation, it raises some issues such as (i) "optimal" window choice for analysis, (ii) existence and
determination of an inverse transformation, (iii) performance of analysis-modification-synthesis, or reconstruction
of selected components of the time-frequency plane and (iv) redundancy controllability for low-cost applications, e.g. real-time computations. We address some of these issues, as well as the less often mentioned problem of transform symmetry in the inverse, through oversampled FBs and their optimized inverse(s) in a slightly more general setting than the discrete windowed Fourier transform.
Signals and images in industrial applications are often subject to strong disturbances and thus require robust
methods for their analysis. Since these data are often non-stationary, time-scale or time-frequency tools have
demonstrated effectiveness in their handling. More specifically, wavelet transforms and other filter bank generalizations
are particularly suitable, due to their discrete implementation. We have recently investigated a specific
family of filter banks, the M-band dual-tree wavelet, which provides state of the art performance for image
restoration. It generalizes an Hilbert pair based decomposition structure, first proposed by N. Kingsbury and
further investigated by I. Selesnick. In this work, we apply this frame decomposition to the analysis of two
examples of signals and images in an industrial context: detection of structures and noises in geophysical images
and the comparison of direct and indirect measurements resulting from engine combustion.
KEYWORDS: Wavelets, Image compression, Electronic filtering, Signal to noise ratio, Data compression, Signal processing, Linear filtering, Wavelet transforms, Nonlinear filtering, Oceanography
Generalized Lapped Orthogonal Transform based image coder is used to compress 2D seismic data sets. Its performance is compared to the results using wavelet-based image coder. Both algorithms use the same state-of-the-art zerotree coding for consistency and fair comparison. Several parameters such as filter length and objective cost function are varied to find the best suited filter banks. It is found that for raw data, filter bank with long overlapping filters should be used for processing signals along the time direction whereas filter bank with short filters should be used for processing signal along the distance direction. This combination yields the best results.
Conference Committee Involvement (5)
Image Processing: Machine Vision Applications VI
5 February 2013 | Burlingame, California, United States
Image Processing: Machine Vision Applications V
25 January 2012 | Burlingame, California, United States
Image Processing: Machine Vision Applications IV
25 January 2011 | San Francisco Airport, California, United States
Wavelet Applications in Industrial Processing VII
18 January 2010 | San Jose, California, United States
Wavelet Applications in Industrial Processing VI
21 January 2009 | San Jose, California, United States
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