Image processing and data analysis: the multiscale approach
Image processing and data analysis: the multiscale approach
Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging
IEEE Transactions on Information Theory
Wavelet-domain filtering for photon imaging systems
IEEE Transactions on Image Processing
A based Bayesian wavelet thresholding method to enhance nuclear imaging
Journal of Biomedical Imaging
Locally adaptive image denoising by a statistical multiresolution criterion
Computational Statistics & Data Analysis
Simplified noise model parameter estimation for signal-dependent noise
Signal Processing
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In experiments, observations are often modelled as a noisy signal. If the signal is embedded in an additive Gaussian noise, its estimation is often done by finding a wavelet basis that concentrates the signal energy over few coefficients and by thresholding the noisy coefficients. However, in many problems of physics, the recorded data are not modelled by Gaussian noise but as the realisation of a Poisson process. In this case, a method of general Poisson process filtering is used. This widens the Gaussian noise filtering and is operated by a kind of frequency-and-time hard thresholding of Haar wavelet coefficients. Not only the detail coefficients are thresholded but also the coefficients related to the rough approximation. Because of the distribution of the wavelet coefficients, a pair of thresholds is proposed for each coefficient. This filtering is illustrated with spectra from different experiments.