On time-dependent wavelet denoising (original) (raw)
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Bayesian wavelet-based signal estimation using non-informative priors
Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284)
The sparseness and decorrelation properties of the discrete wavelet transform have been exploited to develop powerful signal denoising methods. Most existing schemes involve arbitrary thresholding nonlinearities and ad hoc threshold levels, or computationally expensive signal-adaptive procedures. Furthermore, because the DWT is not a translation-invariant (TI) transform, results of processing depend on the relative alignment between data and wavelets in a complicated manner. In the context of denoising, this non-stationarity can produce undesirable ("pseudo-Gibbs" or "blocking") artifacts. To overcome these deficiencies, we propose a new wavelet-based signal denoising technique derived using the theory of non-informative Bayesian priors. The resulting estimator is TI and employs a very simple fixed non-linear shrinkage/thresholding rule. Remarkably, our new approach is very computationally efficient and performs better than standard methods that are more computationally demanding.
Experiments in Wavelet Shrinkage Denoising
Journal of Computational Methods in Sciences and Engineering
Previous simulation experiments for the comparison of wavelet shrinkage denoising methods have failed to demonstrate significant differences between methods. Such differences have never been clearly demonstrated due to the use of qualitative comparisons or of quantitative comparisons that suffered from insufficient sample size and/or absent confidence intervals for the figure of merit investigated.
A Parameter Selection Method for Wavelet Shrinkage Denoising
BIT Numerical Mathematics, 2000
Thresholding estimators in an orthonormal wavelet basis are well established tools for Gaussian noise removal. However, the universal threshold choice, suggested by Donoho and Johnstone, sometimes leads to over-smoothed approximations. For the denoising problem this paper uses the deterministic approach proposed by Chambolle et al., which handles it as a variational problem, whose solution can be formulated in terms of wavelet shrinkage. This allows us to use wavelet shrinkage successfully for more general denoising problems and to propose a new criterion for the choice of the shrinkage parameter, which we call H-curve criterion. It is based on the plot, for different parameter values, of the B 1 1 (L1)-norm of the computed solution versus the L2-norm of the residual, considered in logarithmic scale. Extensive numerical experimentation shows that this new choice of shrinkage parameter yields good results both for Gaussian and other kinds of noise.
International Journal of Engineering, 2012
This paper presents a comparative analysis of different image denoising thresholding techniques using wavelet transforms. There are different combinations that have been applied to find the best method for denoising. Visual information transmitted in the form of digital images is becoming a major method of communication, but the image obtained after transmission is often corrupted with noise. . The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. Wavelet algorithms are useful tool for signal processing such as image compression and denoising. Image denoising involves the manipulation of the image data to produce a visually high quality image.
A joint inter-and intrascale statistical model for Bayesian wavelet based image denoising
… , IEEE Transactions on, 2002
This paper presents a new wavelet-based image denoising method, which extends a recently emerged "geometrical" Bayesian framework. The new method combines three criteria for distinguishing supposedly useful coefficients from noise: coefficient magnitudes, their evolution across scales and spatial clustering of large coefficients near image edges. These three criteria are combined in a Bayesian framework. The spatial clustering properties are expressed in a prior model. The statistical properties concerning coefficient magnitudes and their evolution across scales are expressed in a joint conditional model. The three main novelties with respect to related approaches are: (1) the interscale-ratios of wavelet coefficients are statistically characterized, and different local criteria for distinguishing useful coefficients from noise are evaluated; (2) a joint conditional model is introduced, and (3) a novel anisotropic Markov Random Field prior model is proposed. The results demonstrate an improved denoising performance over related earlier techniques.