Efficient design of SVD-based 2-D digital filters using specification symmetry and order-selecting criterion

Two-dimensional (2-D) digital filters are widely useful in image processing and other 2-D digital signal processing fields, but designing 2-D digital filters is much more difficult than designing one-dimensional (1-D) ones. This paper provides a new insight into the existing singular value decomposition (SVD)-based design approach in the sense that the SVD-based design can be performed more efficiently by exploiting the new symmetry of the 2-D magnitude specifications. By using the specification symmetry, only half of the 1-D filters (sub-filters) need to be designed, which significantly simplifies the design process and reduces the computer storage required for 1-D sub-filter coefficients. Another novel point of this paper is that an objective criterion is proposed for selecting appropriate sub-filter orders in order to reduce the hardware implementation cost. A design example is given to illustrate the effectiveness of the SVD-based design approach by exploiting specification symmetry and new order-selecting criterion.