Two-dimensional separable filters for optimal reconstruction of JPEG-coded images

Transform coding is a technique used worldwide for image coding, and JPEG has become the most common tool for image compression. In a JPEG decoder, the quantized transform coefficient blocks are usually processed using the inverse discrete cosine transform (DCT) in order to reconstruct an approximation of the original image. The direct and inverse DCT pair can be arranged in the form of a perfect reconstruction filter bank, and it can be shown that, in the presence of quantization of the transform coefficients, the perfect reconstruction synthesis is not the best choice. In this paper, we propose a procedure for the design of separable 2-D synthesis filters that minimize the reconstruction error power for transform coders. The procedure is used to design a family of filters which are used in the decoder instead of the inverse DCT. The appropriate reconstruction filters are selected on the basis of the standard quantization information provided in the JPEG bit stream. We show that the proposed decoding method gives some gain with respect to the usual decoder in most cases, Moreover, it only makes use of the standard information provided by a JPEG bit stream.