L2 vector median filters on arrays with reconfigurable optical buses

In spite of their good filtering characteristics for vector-valued image processing, the usability of vector median filters is limited by their high computational complexity. Given an N × N image and a W × W window, the computational complexity of vector median filter is O(W⁴N²). In this paper, we design three fast and efficient parallel algorithms for vector median filtering based on the 2-norm (L₂) on the arrays with reconfigurable optical buses (AROB). For 1 ⩽ p ⩽ W ⩽ q ⩽ N, our algorithms run in O(W⁴ log W/p⁴), O(W²N²/p ⁴q² log W) and O(1) times using p⁴N² / log W, p⁴q² / log W, and W⁴N² log N processors, respectively. In the sense of the product of time and the number of processors used, the first two results are cost optimal and the last one is time optimal