New approaches to block filtering of images using symmetric convolution and the DST or DCT

New approaches to block filtering of images are presented based on the recently introduced operation of symmetric convolution. Symmetric convolution is a formalized approach to convolving symmetric finite impulse response (FIR) filters with symmetrically extended data. It is efficient because the discrete sine and cosine transforms (DST & DCT) can be used to perform the convolution as a transform-domain multiplication. With proper zero-padding of the input data, symmetric convolution gives the same result as linear convolution. As a consequence, it is now possible to use the overlap-add and overlap-save techniques with DSTs and DCTs in order to efficiently filter large images. An alternative method to conventional block filtering is proposed, whereby the blocks need not be overlapped. This approach is extended for those applications where reduced complexity is needed and the approximation to conventional linear filtering is adequate