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.