Image filtering in the block DCT domain using symmetric convolution

摘要

Processing of images in the transform domain saves computation by avoiding inverse and re-transform operations. In this paper, we present a technique for filtering of images in the transform domain using symmetric convolution in the block DCT space. Due to the application of convolution-multiplication property in the DCT domain, the filtering operation requires significantly less computation than its equivalent in the original signal/image space. To take care of discontinuities along boundaries of blocks, filtering is performed on a larger DCT block composed from adjacent blocks. Subsequently, the filtered DCT block is obtained by decomposing it. The proposed filtering technique achieves the same results of linear convolution in the spatial domain with reduced cost. With the proposed filtering, it is possible to significantly speedup the operation by ignoring some elements in the filtering matrices whose magnitudes are smaller than a threshold value. Typical sparseness of DCT domain input blocks is also considered for further reduction of computational cost. The proposed method uses simple linear operations such as matrix multiplication, which is appropriate for efficient hardware implementations. We also demonstrate its applications in image sharpening and removal of blocking artifacts directly in the compressed domain.