IEEE Transactions on Computers
Numerical Linear Algebra and Applications, Second Edition
Numerical Linear Algebra and Applications, Second Edition
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: image and multidimensional signal processing - Volume V
Image filtering in the compressed domain
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
Symmetric convolution using unitary transform matrices
IEEE Transactions on Signal Processing
Symmetric convolution and the discrete sine and cosine transforms
IEEE Transactions on Signal Processing
The spatial relationship of DCT coefficients between a block andits sub-blocks
IEEE Transactions on Signal Processing
Fast multiresolution image operations in the wavelet domain
IEEE Transactions on Visualization and Computer Graphics
Fast DCT domain filtering using the DCT and the DST
IEEE Transactions on Image Processing
DCT convolution and its application in compressed domain
IEEE Transactions on Circuits and Systems for Video Technology
An efficient method for DCT-domain separable symmetric 2-D linear filtering
IEEE Transactions on Circuits and Systems for Video Technology
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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.