This paper presents a heuristic Learning-based Non-Negativity Constrained Variation (L-NNCV) aiming to search the coefficients of variational model automatically and make the variation adapt different images and problems by supervised-learning strategy. The model includes two terms: a problem-based term that is derived from the prior knowledge, and an image-driven regularization which is learned by some training samples. The model can be solved by classical ε-constraint method. Experimental

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... lts show that: the experimental effectiveness of each term in the regularization accords with the corresponding theoretical proof; the proposed method outperforms other PDE-based methods on image denoising and deblurring.