Rounding transform for lossless image coding

A new transform, called the rounding transform (RT), is introduced which employs a pair of rounding operations namely, rounding up and rounding down operations. The RT is of interest in pyramid data structured coding for progressive and lossless image transmission, since the total number of data to be transmitted is the same as that of the original without overhead bits and since it has the advantages of both implementation with various elementary block sizes and filters. Additionally, the previous methods, reduced difference pyramid (RDP) and hierarchy embedded differential image (HEDI) are proved to be only simple cases of the rounding transform. Computer simulations prove that several kinds of rounding transform can be found, which perform better than the previous methods