An adaptive lapped biorthogonal transform and its application in orientation adaptive image coding

We present the theory and design of an adaptive lapped biorthogonal transform for image coding. The proposed transform consists of basis functions overlapping across adjacent blocks and non-overlapping basis functions, where the basis functions' centers of symmetry are aligned. Because of the alignment, we can use the symmetric extension method at image boundaries when we transform an input image. Next, we show that the optimal non-overlapping basis functions in the minimal mean square error sense can be found by solving an eigenvalue problem without numerical search when the feasible overlapping basis functions are given. This derivation is enabled by the subspace Karhunen-Loeve transform which provides the optimal approximation of an original signal in a given subspace, and which has been proposed by the present authors. We show an orientation adaptive example, where each adaptive transform is characterized by the angle of edges in image blocks. In the encoder, each block is selectively transformed by one of orientation adaptive transforms. Experimental results show that the use of adaptation improves the quality of decoded images. (C) 2002 Elsevier Science B.V. All rights reserved.