A Generalized Gaussian Image Model for Edge-Preserving MAP Estimation Charles Bouman, Ken Sauer This paper introduces a generalized Gaussian Markov random field (GGMRF) model for edge-preserving maximum a posteriori (MAP) image estimation. The GGMRF is a Markov random field with a potential function of the form |Δ|^p, where 1 ≤ p ≤ 2. This model is similar to the generalized Gaussian distribution used in robust detection and estimation. The GGMRF has several desirable properties for MAP estimation, including continuous dependence on the data, invariance to scaling of data, and a solution that lies at the unique local minimum of the a posteriori log likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low dosage transmission tomography. The paper discusses the use of Markov random fields (MRFs) for image estimation, noting that traditional Gaussian MRFs can be too smooth and fail to preserve edges. Non-convex potential functions can lead to unstable MAP estimates. The GGMRF addresses these issues by using a convex potential function, which allows for stable and efficient computation of the MAP estimate. The GGMRF is shown to be scale-invariant, making it suitable for a wide range of image processing applications. The paper also discusses the use of convex potential functions for image estimation, noting that they allow for efficient computation of the MAP estimate. The GGMRF is shown to be effective in image reconstruction from integral projections, particularly in low dosage transmission tomography. The paper compares the performance of the GGMRF with traditional methods, showing that it can produce sharper edges while suppressing noise. The paper concludes that the GGMRF is a promising model for edge-preserving MAP estimation, with the potential to be useful in many other image restoration and reconstruction problems. The GGMRF is shown to be effective in a variety of applications, including statistical tomographic reconstruction, where it can produce high-quality images with sharp edges and reduced noise.A Generalized Gaussian Image Model for Edge-Preserving MAP Estimation Charles Bouman, Ken Sauer This paper introduces a generalized Gaussian Markov random field (GGMRF) model for edge-preserving maximum a posteriori (MAP) image estimation. The GGMRF is a Markov random field with a potential function of the form |Δ|^p, where 1 ≤ p ≤ 2. This model is similar to the generalized Gaussian distribution used in robust detection and estimation. The GGMRF has several desirable properties for MAP estimation, including continuous dependence on the data, invariance to scaling of data, and a solution that lies at the unique local minimum of the a posteriori log likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low dosage transmission tomography. The paper discusses the use of Markov random fields (MRFs) for image estimation, noting that traditional Gaussian MRFs can be too smooth and fail to preserve edges. Non-convex potential functions can lead to unstable MAP estimates. The GGMRF addresses these issues by using a convex potential function, which allows for stable and efficient computation of the MAP estimate. The GGMRF is shown to be scale-invariant, making it suitable for a wide range of image processing applications. The paper also discusses the use of convex potential functions for image estimation, noting that they allow for efficient computation of the MAP estimate. The GGMRF is shown to be effective in image reconstruction from integral projections, particularly in low dosage transmission tomography. The paper compares the performance of the GGMRF with traditional methods, showing that it can produce sharper edges while suppressing noise. The paper concludes that the GGMRF is a promising model for edge-preserving MAP estimation, with the potential to be useful in many other image restoration and reconstruction problems. The GGMRF is shown to be effective in a variety of applications, including statistical tomographic reconstruction, where it can produce high-quality images with sharp edges and reduced noise.