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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. Experimentaldoi:10.4208/nmtma.2017.m1653 fatcat:d2p476fv4zbqbcssx5j6tjttdu