The paper presents a Markov random field (MRF) model, specifically the generalized Gaussian Markov random field (GGMRF), designed to allow realistic edges in maximum a posteriori (MAP) image estimates while maintaining stable solutions. The GGMRF model is based on a generalized Gaussian distribution, which is similar to the distribution used in robust detection and estimation. This model satisfies several desirable properties for MAP estimation, including continuous dependence on the data, invariance to data scaling, and a 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, where it effectively suppresses photon counting noise and sharpens edges without blurring. The paper also discusses the connection between median filtering and MAP estimation using the GGMRF prior, and provides experimental results showing the effectiveness of the GGMRF in reconstructing images from integral projections. The GGMRF is particularly effective in handling images with sharp transitions and is promising for various image restoration and reconstruction problems. However, the slow convergence of the MAP estimate with small values of the parameter \( p \) is a significant challenge that requires further research to address.The paper presents a Markov random field (MRF) model, specifically the generalized Gaussian Markov random field (GGMRF), designed to allow realistic edges in maximum a posteriori (MAP) image estimates while maintaining stable solutions. The GGMRF model is based on a generalized Gaussian distribution, which is similar to the distribution used in robust detection and estimation. This model satisfies several desirable properties for MAP estimation, including continuous dependence on the data, invariance to data scaling, and a 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, where it effectively suppresses photon counting noise and sharpens edges without blurring. The paper also discusses the connection between median filtering and MAP estimation using the GGMRF prior, and provides experimental results showing the effectiveness of the GGMRF in reconstructing images from integral projections. The GGMRF is particularly effective in handling images with sharp transitions and is promising for various image restoration and reconstruction problems. However, the slow convergence of the MAP estimate with small values of the parameter \( p \) is a significant challenge that requires further research to address.