Efficient design of 2-D nonseparable filters of low complexity

By using Semi-Definite Programming (SDP) as a tool, a new deign for Two-Dimensional (2-D) Diamond-Shaped (DS) filters is developed. Surprisingly, the diamond shape of the filter is exactly expressed by using simple 2-D trigonometric polynomial curves of second order. In contrast to the high-order polynomial transformation based methods, the order of the designed filters is kept moderate with no performance sacrifices. Unlike conventional non-separable 2-D filters, the designed filters allow fast digital implementation despite being nonseparable and hence they are of low complexity. Numerical Simulations with application to quincunx image sampling are also performed to illustrate the viability of our method.