This paper describes a discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a real-valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. Two forms of the transform are presented. The first form is defined for discrete-time signals defined on all of Z. The second form is defined for discrete-time signals of finite-length and can be implemented efficiently with FFTs. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e.g., three to four times overcomplete) being sufficient for the analysis/synthesis functions to be well localized.

Wavelet Transform With Tunable Q-Factor

Most wavelet transforms used in practice are based on integer sampling factors. Wavelet transforms based on rational sampling factors offer in principle the potential for time-scale signal representations having a finer frequency resolution. Previous work on rational wavelet transforms and filter banks includes filter design methods and frequency domain implementations. We present several specific examples of Daubechies-type filters for a discrete orthonormal rational wavelet transform (FIR filters having a maximum number of vanishing moments) obtained using Grobner bases. We also present the design of overcomplete rational wavelet transforms (tight frames) with FIR filters obtained using polynomial matrix spectral factorization.

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Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors

Publisher Summary This chapter discusses the scalable video coding for adaptive streaming applications. The transmission of multimedia content over Internet Protocol (IP) networks, such as the Internet and wireless networks, has been growing steadily over the past few years. Moreover, multimedia streaming and the set of applications that rely on streaming are expected to continue growing. To achieve a higher level of quality and further proliferation of IP video, many technical challenges have to be addressed in the two areas of video coding and networking. A framework that addresses both the video coding and the networking challenges associated with IP-based video streaming is scalability. Scalable techniques try to avoid simulcast solutions in which several encoders run in parallel. Simulcast solutions usually require knowledge of the network and decoder capabilities in advance to select the best encodings. There are three basic types of scalability in scalable video coding: spatial, temporal, and quality (or SNR) scalabilities. In a spatial scalable scheme, full decoding leads to high spatial resolution, while partial decoding leads to reduced spatial resolutions (reduction of the format). In a temporal scalable scheme, partial decoding provides lower decoded frame rates. In an SNR scalable scheme, temporal and spatial resolutions are kept the same, but the video quality (SNR) varies depending on how much of the bit stream is decoded.

Scalable Video Coding for Adaptive Streaming Applications

A new M-channel DFT filter bank with its analysis and synthesis parts being modified is proposed for arbitrary image scaling, whereby down/up sampling kernels are newly introduced along with a compactly supported sampling function of degree 2. In particular, while only an even number of channels is allowed in the conventional MDFT FB, arbitrary (even/odd) number of channels can be applied in the proposed approach. Furthermore, it is shown that images of arbitrary size can be obtained from an original image without changing the number of channels. Finally, simulation results demonstrate that high-quality images of arbitrary size can be achieved by the proposed approach.

Design of a new DFT filter bank with modified sampling kernels and its application to arbitrary image scaling

A new approach to arbitrary scaling of high quality images is proposed, whereby a 2-D M-channel DFT filter bank is designed along with its synthesis part being modified on the basis of a compactly supported sampling function. For that purpose, the 2-D down/up-sampling formulae in a closed form are derived and utilized. Also, an optimized adaptive interpolation technique is employed to compensate for quality degradation arising in scaled images. Finally, simulation results demonstrate that high quality images of arbitrary size can be obtained from the original image.

Arbitrary scaling of images using an M-channel DFT filter bank with optimized adaptive interpolation kernels

Subband image coding with classical wavelet transforms inherently provides dyadic scalability since the low-pass approximation band can be used as a half-sized version of the original image The multiresolution approach further provides scalability factors that are powers of two, but no other factors can be easily reached On the other hand, a hierarchical scheme based on M-bandtransforms will lead only to scalability factors that are powers of M In this letter, we present how an M-band synthesis filter bank can be modified in order to directly reconstruct an output image of a resolution reduced by a factor M/P, where P is an integer lower than M As the analysis filter bank is not modified, this technique allows the design of subband decoding schemes that support fractional scalability With this feature, the same compressed bitstream can be directly decoded by different receivers at several resolutions, depending on their computational and bandwith capabilities

G. Pau

Papers

Modified M-band synthesis filter bank for fractional scalability of images