Edge-preserving filtering by projection onto L0 gradient constraint

• Published in: Proceedings of the ... IEEE International Conference on Acoustics, Speech and Signal Processing (1998) pp. 1492 - 1496
• Main Author: Ono, Shunsuke
• Format: Conference Proceeding
• Language: English; Japanese
• Published: IEEE 01.03.2017
• Subjects: Algorithm design and analysis; constrained optimization; Convex functions; edge-preserving filtering; Filtering; Image edge detection; Indexes; L 0 gradient; Minimization; nonconvex optimization; Optimization
• ISSN: 2379-190X
• DOI: 10.1109/ICASSP.2017.7952405

We propose an edge-preserving filtering method with a novel use of the L 0 gradient. Our method, termed as the L 0 gradient projection, is formulated as the minimization of a quadratic data-fidelity to an input image subject to the constraint that the L 0 gradient, the number of non-zero gradients, of the output image is less than a user-given parameter α. This strategy is much more intuitive than the conventional approach, the L 0 gradient minimization, that minimizes the sum of the L 0 gradient plus the quadratic data-fidelity, because one can directly impose a desired degree of flatness by α, which is impossible in the L 0 gradient minimization. We also provide an efficient algorithm based on the so-called alternating direction method of multipliers for solving the nonconvex optimization problem associated with the L 0 gradient projection. The utility of the L 0 gradient projection is illustrated by experiments.