Angular regularization of vector-valued signals

A new class of pair-wise regularizers is proposed for vector-valued signals, including several new regularizers that penalize the angular difference between neighboring vectors. The pair-wise model is a generalization of the conventional difference model that includes discretized Tikhonov, Li, and Total Variation (TV) as special cases. Whereas Tikhonov and TV regularization have become popular for encouraging signal values to be smooth or piecewise smooth, respectively, angular regularizers are pro posed to encourage vector directions to be smooth or piecewise smooth. The regularizers are simple, effective, and general, making them easily applicable to a wide array of problems. Experimental results demonstrate the method´s effectiveness in denoising vector fields and color images.