Two dimensional FRS-LMS adaptive filter (2D FRS-LMS)

A new 2D frequency-response-shaped least mean square (2D FRS-LMS) adaptive filter is proposed by developing the 1D FRS-LMS. The new algorithm reuses data in both horizontal and vertical directions within the space plane to update the weight vector of the filter. Further, the proposed algorithm involves the multiplication of the filter coefficient vector by a variable matrix in the coefficient updating process. The new 2D FRS-LMS weight updating equation is derived and its performance is compared with that of the two dimensional LMS (2D LMS) and 2D leaky-LMS algorithms regarding image enhancement. The new algorithm gives improved performance over the other algorithms. The proposed 2D FRS-LMS is particularly useful in image processing, especially in data compression and image enhancement applications.