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It is important and necessary to take account of the non-zero pattern in image sparsity representation. In this paper, we present an image restoration model by introducing a novel edge-continuous overlapping group sparsity regularizer (EC-OGS), based on our observation that the non-zero entries in an image gradient domain often distribute along its edges. The model is solved by the ADMM (alternating direction method of multipliers), where a fast novel algorithm is proposed for computing the proximal operator in solving the subproblem with EC-OGS regularizer. The proposed model can be applied to various image restoration tasks including denoising, deblurring, and edge-detecting. The numerical experiments demonstrate the effectiveness of our method in terms of PSNR, visual effect and edge preserving. [ABSTRACT FROM AUTHOR]