Ali N. Akansu

Orthogonal transmultiplexers in communication: a review

This paper presents conventional and emerging applications of orthogonal synthesis/analysis transform configurations (transmultiplexer) in communications. It emphasizes that orthogonality is the underlying concept in the design of many communication systems. It is shown that orthogonal filter banks (subband transforms) with proper time-frequency features can play a more important role in the design of new systems. The general concepts of filter bank theory are tied together with the application-specific requirements of several different communication systems. Therefore, this paper is an attempt to increase the visibility of emerging communication applications of orthogonal filter banks and to generate more research activity in the signal processing community on these topics.

Full length article: Emerging applications of wavelets: A review

Although most of its popular applications have been in discrete-time signal processing for over two decades, wavelet transform theory offers a methodology to generate continuous-time compact support orthogonal filter banks through the design of discrete-time finite length filter banks with multiple time and frequency resolutions. In this paper, we first highlight inherently built-in approximation errors of discrete-time signal processing techniques employing wavelet transform framework. Then, we present an overview of emerging analog signal processing applications of wavelet transform along with its still active research topics in more matured discrete-time processing applications. It is shown that analog wavelet transform is successfully implemented in biomedical signal processing for design of low-power pacemakers and also in ultra-wideband (UWB) wireless communications. The engineering details of analog circuit implementation for these continuous-time wavelet transform applications are provided for further studies. We expect a flurry of new research and technology development activities in the coming years utilizing still promising and almost untapped analog wavelet transform and multiresolution signal representation techniques.

A class of fast Gaussian binomial filters for speech and image processing

The authors present an efficient, in-place algorithm for the batch processing of linear data arrays. These algorithms are efficient, easily scaled, and have no multiply operations. They are suitable as front-end filters for a bank of quadrature mirror filters and for pyramid coding of images. In the latter application, the binomial filter was used as the low-pass filter in pyramid coding of images and compared with the Gaussian filter devised by P.J. Burt (Comput. Graph. Image Processing, vol.16, p.20-51, 1981). The binomial filter yielded a slightly larger signal-to-noise ratio in every case tested. More significantly, for an (L+1)*(L+1) image array processed in (N+1)*(N+1) subblocks, the fast Burt algorithm requires a total of 2(L+1)/sup 2/N adds and 2(L+1)/sup 2/ (N/2+1) multiplies. The binomial algorithm requires 2L/sup 2/N adds and zero multiplies. >

A subspace method for blind channel identification in OFDM systems

It has been shown that cyclostationarity in the received signal allows the receiver to blindly identify the channel impulse response using only second-order statistics. In orthogonal frequency-division multiplexing (OFDM) systems, cyclostationarity is embedded at the transmitter due to cyclic prefix. In this paper, a subspace approach based on second-order statistics is proposed for blind channel identification in OFDM systems. We derive a sufficient condition that guarantees all the channels to be identifiable no matter what their zero locations are. Computer simulations demonstrate the superior performance of the proposed algorithm over methods reported earlier in the literature.

Unequal error protection of SPIHT encoded image bit streams

A derivative of the set partitioning into hierarchical trees (SPIHT) image coding method, which generates substreams with different error-resilience properties, is proposed. By dividing the image bit stream into three classes, substreams with different immunity properties are obtained. The unequal protection of these substreams with different channel coding rates improves the overall performance of the method against channel errors. Simulation results show the superiority of the proposed method over some of the state-of-the-art methods.

Adaptive subband transforms in time-frequency excisers for DSSS communications systems

A smart time-frequency exciser for DS-SS communications is proposed in this correspondence. This technique utilizes the concept of uncertainty in time-frequency analysis of signals. It brings the novel concept of domain switchable signal processing. Hence, the adaptive time-frequency (ATF) exciser has the capability of deciding the domain of the interference cancellation. Additionally, adaptive subband transforms are utilized for frequency domain excision. For time-domain excision, the ATF excision algorithm utilizes a sliding time window to reject the nonstationary, pulsed (time-localized) interference. It is shown that the proposed adaptive time-frequency exciser-based DS-SS communications receiver drastically outperforms the existing systems. Its performance is nearly optimal and very robust to the inter and intradomain variations of the undesired signal.

On-signal decomposition techniques

Well-known block transforms and perfect reconstruction orthonormal filter banks are evaluated based on their frequency behavior and energy compaction. The filter banks outperform the block transforms for the signal sources considered. Although the latter are simpler to implement and already the choice of the existing video coding standards, filter banks with simple algorithms may well become the signal decomposition technique for the next generation video codecs, which require a multiresolution signal representation.

The Binomial QMF-Wavelet Transform for Multiresolution Signal Decomposition

Perfect reconstruction quadrature mirror filters (PR QMF’s) have been proposed as structures suitable for hierarchical subband coding [ ll-[4], and also for multiresolution signal decomposition as might be used in image pyramid coding [5]. More recently, multiresolution signal decomposition methods are being examined from the standpoint of the discrete wavelet transform for continuous-time signals [6]-[8]. In this paper, we describe a class of orthogonal binomial filters that provide basis functions for a perfect reconstruction bank of finite impulse response QMF’s. The orthonormal wavelet filters derived by Daubechies 171 from a discrete wavelet transform approach are shown to be the same as the solutions inherent in the binomial-based filters. The energy compaction performance of the binomial QMF decomposition is computed and shown to be better than the DCT for the Markov source models, as well as real-world images considered. The proposed binomial structure is efficient, simple to implement on VLSI, and suitable for multiresolution signal decomposition and coding applications.

A generalized parametric PR-QMF design technique based on Bernstein polynomial approximation

A generalized, parametric, perfect-reconstruction quadrature-mirror-filter (PR-QMF) design technique based on Bernstein polynomial approximation in the magnitude-square domain is presented. The parametric nature of this solution provides useful insights to the PR-QMF problem. Several well-known orthonormal wavelet filters, PR-QMFs, are shown to be the special cases of the proposed technique. Energy compaction performances of a few popular signal decomposition techniques are presented for AR(1) signal sources. It is observed that the hierarchical QMF filter banks considered outperform the block transforms as expected. >

Capacity estimates for data hiding in compressed images

In this paper, we present an information-theoretic approach to obtain an estimate of the number of bits that can be hidden in still images, or, the capacity of the data-hiding channel.We show how the addition of the message signal or signature in a suitable transform domain rather than the spatial domain can significantly increase the channel capacity. Most of the state-of-the-art schemes developed thus far for data-hiding have embedded bits in some transform domain, as it has always been implicitly understood that a decomposition would help. Though most methods reported in the literature use DCT or wavelet decomposition for data embedding, the choice of the transform is not obvious.We compare the achievable data-hiding capacities for different decompositions like DCT, DFT, Hadamard, and subband transforms and show that the magnitude DFT decomposition performs best among the ones compared.