Wavelets, Gaussian mixtures and Wiener filtering
Signal Processing
Three Novel Models of Threshold Estimator for Wavelet Coefficients
WAA '01 Proceedings of the Second International Conference on Wavelet Analysis and Its Applications
Wavelet denoising of poisson-distributed data and applications
Computational Statistics & Data Analysis
DeQuant: a flexible multiresolution restoration framework
Signal Processing
DeQuant: a flexible multiresolution restoration framework
Signal Processing
Fast interscale wavelet denoising of Poisson-corrupted images
Signal Processing
IEEE Transactions on Image Processing
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Restoration of Poissonian images using alternating direction optimization
IEEE Transactions on Image Processing
Denoising by anisotropic diffusion of independent component coefficients
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
Adaptive noise reduction of scintigrams with a wavelet transform
Journal of Biomedical Imaging
Poisson image denoising using geometric platelets and geometric quadlets
Signal Processing
Simplified noise model parameter estimation for signal-dependent noise
Signal Processing
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Many imaging systems rely on photon detection as the basis of image formation. One of the major sources of error in these systems is Poisson noise due to the quantum nature of the photon detection process. Unlike additive Gaussian white noise, the variance of Poisson noise is proportional to the underlying signal intensity, and consequently separating signal from noise is a very difficult task. In this paper, we perform a novel gedankenexperiment to devise a new wavelet-domain filtering procedure for noise removal in photon imaging systems. The filter adapts to both the signal and the noise, and balances the trade-off between noise removal and excessive smoothing of image details. Designed using the statistical method of cross-validation, the filter is simultaneously optimal in a small-sample predictive sum of squares sense and asymptotically optimal in the mean-square-error sense. The filtering procedure has a simple interpretation as a joint edge detection/estimation process. Moreover, we derive an efficient algorithm for performing the filtering that has the same order of complexity as the fast wavelet transform itself. The performance of the new filter is assessed with simulated data experiments and tested with actual nuclear medicine imagery