Dietary methionine restriction (MR) has many positive effects on metabolic health.

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In this paper, we examine the wavelet characterization of Hardy space H 1 , and show that the H 1 -norm is a good choice for modelizing the oscillating patterns. Furthermore, we give the discrete representation of H 1 -norm by using wavelet coefficients, and apply it to the variational image decomposition models. Finally, we give the iterative algorithm, and present various numerical results on images to demonstrate the potential of our methods.