Linear spatial filter design for implementation on the CNN Universal Machine

Linear spatial filtering is an important component of most image and video processing algorithms Therefore, when designing CNN Universal Machine (CNN-UM) algorithms for image and video applications, it would be useful to be able to implement desired filtering operations on the hardware. Although it has been shown that any convolution mask can, in principle, be implemented by a series of 3×3 template operations, such methods are time-consuming and error-prone. In this paper we investigate the use of simple CNN-UM algorithms involving only three filtering stages and using only 3×3 A- and B-templates to approximate desired filter transfer functions. The transfer functions for the structures are derived and a reduced parameterization is introduced. This form is conducive to optimization. Several examples are given wherein filters are designed to approximate a desired transfer function