On filter bank and transform design with the lifting scheme.

摘要

The theory of filter banks and linear transform has found wide applications in image/video compression, signal processing, analysis, and communications. A powerful tool in the design of filter banks and transforms is the lifting scheme whose construction not only offers robust and efficient implementation structures, but also can lower the computational complexity and minimize the number of free parameters in an unconstrained optimization design.; In this dissertation, we first concentrate on the lifting-based design of critically sampled filter bank and its applications in image and video compression. We present a systematic lifting-based design of multiplierless approximation of the Inverse Discrete Cosine Transform called binIDCT . The binIDCT can be implemented in a fast, multiplier-free manner, and allow computational scalability with different accuracy-versus-complexity trade-offs. It enables a simple construction of the corresponding multiplierless forward DCT, providing bit-exact reconstruction if pairing with the corresponding binIDCT scheme. Unlike other fixed-point IDCT algorithms in the literature, our complexity-distortion optimal solutions can provide a large family of standard-compliant binIDCTs, from 16-bit approximations catering to portable computing to ultra-high-accuracy 32-bit versions that virtually eliminate any drifting effect when pairing with the 64-bit floating-point IDCT at the encoder. They can lead to extreme high quality image and video reconstructions in real image/video coders.; The Laplacian pyramid (LP) is another signal decomposition technique that is very popular in image-processing and computer vision. It provides an overcompleted signal representation, thus can be treated as an oversampled filter bank. In the second part of this dissertation, we present a lifting-based factorization for the LP decomposition, and propose a generic lifting-based reconstruction algorithm to characterize all synthesis banks yielding the perfect reconstruction property. Compared to other LP reconstruction algorithms in the literature, our proposed reconstruction scheme contains M times fewer number of free parameters for a LP with decimation factor of M. A special lifting-based LP reconstruction scheme is also derived from our generic LP reconstruction. It not only allows flexible choices of low-pass filters to suppress aliasing in the low resolution images efficiently, but also presents an efficient FB that leads to improvements over the usual LP method for signal reconstruction in the presence of noise.