Isolating neighbor´s contribution towards image filtering in the block DCT space

In this work, we present a simple expression relating the input, output and the filter responses in the block DCT space by isolating contributions of each neighboring block. The proposed technique considers only filters with non-causal symmetric response. The method provides the exact computation of the linear convolution in the compressed domain. Though it is computationally less efficient than existing techniques, the technique is simpler to implement and is suitable for parallel implementation. Further, it also provides a novel framework for computing with both sparse and non-sparse data at the same time and thus reducing the computational requirement substantially with significant improvement in the quality of the output.