Ten lectures on wavelets
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Mathematics and Physics of Emerging Biomedical Imaging
Mathematics and Physics of Emerging Biomedical Imaging
A based Bayesian wavelet thresholding method to enhance nuclear imaging
Journal of Biomedical Imaging
IEEE Transactions on Image Processing
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
Adaptive wavelet thresholding for image denoising and compression
IEEE Transactions on Image Processing
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A method to improve the signal-to-noise-ratio (SNR)of positron emission tomography (PET) scans is presented. A wavelet-based image decomposition technique decomposes an image into two parts, one which primarily contains the desired restored image and the other primarily the remaining unwanted portion of the image. Because the method is based on a texture extraction model that identifies the desired image in the space of bounded variation, these restorations are approximations of piecewise constant images, and are referred to as the cartoon part of the image. Here an approximation using a wavelet decomposition is used which allows solutions to be computed very efficiently. To process 3-D volume data a slice by slice approach in all three directions is adopted. Using a redundant discrete wavelet transform, 3-D restorations can be efficiently computed on standard desktop computers. The method is illustrated for PET images which have been reconstructed from simulated data using the expectation maximization algorithm. When post-processed by the presented wavelet decomposition they show a significant increase in SNR. It is concluded that the new wavelet based method can be used as an alternative to the well established de-noising of PET scans by smoothing with a Gaussian point spread function. In particular, if the volume data are reconstructed using the EM algorithm with a larger number of iterations than the number of iterations that would be used without post-processing, the 3-D images are sharper and show more detail. A MATLAB® based graphical user interface is provided that allows easy exploration of the impact of parameter choices.