The Johns Hopkins University

Whiting School of Engineering

Department of Electrical and Computer Engineering

On Filter Bank and Transform Design with the Lifting Scheme

A Dissertation Defense by

LIJIE LIU

Graduate Research Assistant

Electrical and Computer Engineering

Abstract:

The theory of filter bank and linear transform has found wide applications in audio/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 unconstrained optimization design.

In this dissertation, we first concentrate on lifting-based design for critically sampled filter bank and its applications in image and video compression. We present a systematic lifting-based design of multiplier less approximation of the Inverse Discrete Cosine Transform, which is called binIDCT. The binIDCT can be implemented in a fast, multiplier-free manner, and allows computational scalability with different accuracy-versus-complexity trade-offs. It enables a simple construction of the corresponding multiplier less 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 has found wide applications in image processing and computer vision. It provides an over complete 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 with other LP reconstruction algorithms in the literature, our proposed reconstruction contains M times less 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 choosing the 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 reconstruction in the presence of noise.

Wednesday, October 10, 2007

10:00 a.m.

Barton Hall 225

FOR DISABILITY INFORMATION

CONTACT: Candace Abel (410) 516-7031 cabel@jhu.edu