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In this study, we propose a new approach to reconstruction of the remote sensing images degraded by an image formation system of limited spatial resolution and contaminated with noise. The proposed method employs the idea of combining the image reconstruction strategies with different regularization paradigms. On one hand, we propose to apply the maximum entropy (ME) statistical regularization paradigm for nonlinear image reconstruction, and on the other hand, we make use of the descriptive regularization paradigm of the variational analysis (VA) method to perform image post-processing aimed at the enhanced localization of the homogeneous image zones with edge preservation. The advantages of both the ME and VA regularization approaches are attained via aggregating these two strategies for image reconstruction and noise reduction into the new fused variational analysis maximum entropy (VAME) method for nonlinear reconstructive computational post-processing of the remote sensing imagery. We propose, also, an efficient scheme for computational implementation of the new VAME method that employs the iterative structure of the modified Hopfield-type neural network. The efficiency of the proposed VAME method is illustrated through computer simulations.