Linear regression models for DCT domain approximate filtering and deblurring

This paper presents two linear regression models by exploring the relationships between DCT coefficients of the original image and filtered image. The first model is to scale the DCT coefficients of the original image in order to approximate the operation of 2-D spatial domain filtering. The second model is to predict the original image from the filtered image in a similar manner. We show that the first model is used for DCT domain filtering, while the second model can be used for fast DCT domain image deblurring. Both of them are easy to implement on compressed formats of DCT-based compression methods (JPEG, MPEG, H.26X) by using decoding quantization tables that are different from the encoding quantization tables.