A class of lapped transforms for image coding, which are characterized by variable-length synthesis filters, is introduced. In this class, the synthesis filter bank (FB) is first defined with an arbitrary combination of finite impulse response synthesis filters of perfect reconstruction FBs. An analysis FB is then obtained using direct matrix inversion or iterative implementation of Neumann series expansion. Moreover, to improve compression, we introduce a unitary transform that follows the analysis FB. This class enables a greater freedom of design than previously presented variable-length lapped transforms. We illustrate several design examples and present experimental results for image coding, which indicate that the proposed transforms are promising and comparable with conventional subband transforms including wavelets.

The theory and design for a novel class of a variable-length lapped transform are presented. In this class, the synthesis filter bank is firstly defined with arbitrary combination of FIR filters, giving much freedom of design compared to previously presented variable-length lapped transforms. The analysis filter bank is then obtained as the inverse of the synthesis bank by the Neumann series expansion to achieve the perfect reconstruction. Moreover, by introducing a unitary transform, we improve the compression performance of the analysis bank. We provide several design examples and experimental results of image coding, which show that the proposed transform is promising and comparable with conventional subband transforms including wavelets.