DCT convolution and its application in compressed domain

Conventional processing of JPEG or MPEG compressed image or video data involves first decompressing the data and applying the desired processing function, and then the processed data are recompressed for the purposes of transmission or storage. We propose an alternate processing pipeline which involves direct manipulation of the JPEG or MPEG compressed domain representation to achieve the desired spatial domain processing. For direct manipulation in the compressed domain, we develop a discrete cosine transform (DCT)-domain convolution theorem which besides exploiting the sparseness of the DCT-domain representation also exploits the orthogonality and symmetry in the DCT-domain representation. These properties lead to efficient compressed domain-based processing methods unlike their spatial domain counterparts, where such properties are not available. This theorem can be used in a variety of image and video editing functions when the image and video data are available only as a JPEG or MPEG bitstream. We illustrate the use of the DCT-domain convolution theorem in a typical video editing application such as video bluescreen editing