Learning Compact Partial Differential Equations for Color Images with Efficiency

Abstract

Learning Partial Differential Equations (LPDEs) from training data for particular tasks has been successfully applied to many image processing problems. In this paper, we aim to learn compact Partial Differential Equations (LCPDEs) for color image tasks by proposing a more effective algorithm. The LCPDEs system is formulated as a linear combination of fundamental differential invariants and simplified by omitting the PDE which works as an indicate function. We replace L2-norm with Ll-norm to regularize the coefficients with respect to the invariants. As the objective function is non-smooth, we resort to proximal algorithm to optimize it, which ensures convergence in an at least sub-linear rate. Experiments demonstrate the advantages of the proposed method over other PDE-based methods in terms of both quality and efficiency.