New Transforms Tightly Bounded by DCT and KLT

It is well known that the discrete cosine transform (DCT) and Karhunen-Loève transform (KLT) are two good representatives in image and video coding: the first can be implemented very efficiently while the second offers the best R-D coding performance. In this work, we attempt to design some new transforms with two goals: i) approaching to the KLT´s R-D performance and ii) maintaining the implementation cost no bigger than that of DCT. To this end, we follow a cascade structure of multiple butterflies to develop an iterative algorithm: two out of N nodes are selected at each stage to form a Givens rotation (which is equivalent to a butterfly); and the best rotation angle is then determined by maximizing the resulted coding gain. We give the closed-form solutions for the node-selection as well as the angle-determination, together with some design examples to demonstrate their superiority.