An augmented Lagrangian method for fast gradient vector flow computation

Gradient vector flow (GVF) and its generalization have been widely applied in many image processing applications. The high cost of GVF computation, however, has restricted their potential applications to images with large size. In this paper, motivated by progress in fast image restoration algorithms, we reformulate the GVF computation problem as a convex optimization model with an equality constraint, and solve it using a fast algorithm, inexact augmented Lagrangian method (ALM). With fast Fourier transform (FFT), we provide a novel simple and efficient algorithm for GVF computation. Experimental results show that the proposed method can improve the computational speed by an order of magnitude, and is even more efficient for images with large sizes.