Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning an Integral Equation Approximation to Nonlinear Anisotropic Diffusion in Image Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Anisotropic Diffusion PDE for Noise Reduction and Thin Edge Preservation
ICIAP '99 Proceedings of the 10th International Conference on Image Analysis and Processing
A local update strategy for iterative reconstruction fromprojections
IEEE Transactions on Signal Processing
Mean curvature evolution and surface area scaling in image filtering
IEEE Transactions on Image Processing
Adaptive wavelet graph model for Bayesian tomographic reconstruction
IEEE Transactions on Image Processing
A well-balanced flow equation for noise removal and edge detection
IEEE Transactions on Image Processing
Noise removal with Gauss curvature-driven diffusion
IEEE Transactions on Image Processing
A Nonlinear Probabilistic Curvature Motion Filter for Positron Emission Tomography Images
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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The basic mathematical problem behind PET is an inverse problem. Due to the inherent ill-posedness of this inverse problem, the reconstructed images will have noise and edge artifacts. A roughness penalty is often imposed on the solution to control noise and stabilize the solution, but the difficulty is to avoid the smoothing of edges. In this paper, we propose two new types of Bayesian one-step-late reconstruction approaches which utilize two different prior regularizations: the mean curvature (MC) diffusion function and the Gauss curvature (GC) diffusion function. As they have been studied in image processing for removing noise, these two prior regularizations encourage preserving the edge while the reconstructed images are smoothed. Moreover, the GC constraint can preserve smaller structures which cannot be preserved by MC. The simulation results show that the proposed algorithms outperform the quadratic function and total variation approaches in terms of preserving the edges during emission reconstruction.