The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a` trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement

Broadband adaptive beamforming with low complexity and frequency invariant response

This thesis proposes different methods to reduce the computational complexity as well as increasing the adaptation rate of adaptive broadband beamformers. This is performed exemplarily for the generalised sidelobe canceller (GSC) structure. The GSC is an alternative implementation of the linearly constrained minimum variance beamformer, which can utilise well-known adaptive filtering algorithms, such as the least mean square (LMS) or the recursive least squares (RLS) to perform unconstrained adaptive optimisation.A direct DFT implementation, by which broadband signals are decomposed into frequency bins and processed by independent narrowband beamforming algorithms, is thought to be computationally optimum. However, this setup fail to converge to the time domain minimum mean square error (MMSE) if signal components are not aligned to frequency bins, resulting in a large worst case error. To mitigate this problem of the so-called independent frequency bin (IFB) processor, overlap-save based GSC beamforming structures have been explored. This system address the minimisation of the time domain MMSE, with a significant reduction in computational complexity when compared to time-domain implementations, and show a better convergence behaviour than the IFB beamformer. By studying the effects that the blocking matrix has on the adaptive process for the overlap-save beamformer, several modifications are carried out to enhance both the simplicity of the algorithm as well as its convergence speed. These modifications result in the GSC beamformer utilising a significantly lower computational complexity compare to the time domain approach while offering similar convergence characteristics.In certain applications, especially in the areas of acoustics, there is a need to maintain constant resolution across a wide operating spectrum that may extend across several octaves. To attain constant beamwidth is difficult, particularly if uniformly spaced linear sensor array are employed for beamforming, since spatial resolution is reciprocally proportional to both the array aperture and the frequency. A scaled aperture arrangement is introduced for the subband based GSC beamformer to achieve near uniform resolution across a wide spectrum, whereby an octave-invariant design is achieved. This structure can also be operated in conjunction with adaptive beamforming algorithms. Frequency dependent tapering of the sensor signals is proposed in combination with the overlap-save GSC structure in order to achieve an overall frequency-invariant characteristic. An adaptive version is proposed for frequency-invariant overlap-save GSC beamformer. Broadband adaptive beamforming algorithms based on the family of least mean squares (LMS) algorithms are known to exhibit slow convergence if the input signal is correlated. To improve the convergence of the GSC when based on LMS-type algorithms, we propose the use of a broadband eigenvalue decomposition (BEVD) to decorrelate the input of the adaptive algorithm in the spatial dimension, for which an increase in convergence speed can be demonstrated over other decorrelating measures, such as the Karhunen-Loeve transform. In order to address the remaining temporal correlation after BEVD processing, this approach is combined with subband decomposition through the use of oversampled filter banks. The resulting spatially and temporally decorrelated GSC beamformer provides further enhanced convergence speed over spatial or temporal decorrelation methods on their own

Implementation of accurate broadband steering vectors for broadband angle of arrival estimation

Motivated by accurate broadband steering vector requirements for applications such as broadband angle of arrival estimation, we review fractional delay filter designs. A common feature across these are their rapidly decreasing performance as the Nyquist rate is approached. We propose a filter bank based approach, which operates standard fractional delay filters on a series of frequency-shifted subband signals, such that they appear in the filters’ lowpass region. We demonstrate the appeal of this approach in simulations

Cellular neural networks, Navier-Stokes equation and microarray image reconstruction

Copyright @ 2011 IEEE.Although the last decade has witnessed a great deal of improvements achieved for the microarray technology, many major developments in all the main stages of this technology, including image processing, are still needed. Some hardware implementations of microarray image processing have been proposed in the literature and proved to be promising alternatives to the currently available software systems. However, the main drawback of those proposed approaches is the unsuitable addressing of the quantification of the gene spot in a realistic way without any assumption about the image surface. Our aim in this paper is to present a new image-reconstruction algorithm using the cellular neural network that solves the Navier–Stokes equation. This algorithm offers a robust method for estimating the background signal within the gene-spot region. The MATCNN toolbox for Matlab is used to test the proposed method. Quantitative comparisons are carried out, i.e., in terms of objective criteria, between our approach and some other available methods. It is shown that the proposed algorithm gives highly accurate and realistic measurements in a fully automated manner within a remarkably efficient time

Multiband Spectrum Access: Great Promises for Future Cognitive Radio Networks

Cognitive radio has been widely considered as one of the prominent solutions to tackle the spectrum scarcity. While the majority of existing research has focused on single-band cognitive radio, multiband cognitive radio represents great promises towards implementing efficient cognitive networks compared to single-based networks. Multiband cognitive radio networks (MB-CRNs) are expected to significantly enhance the network's throughput and provide better channel maintenance by reducing handoff frequency. Nevertheless, the wideband front-end and the multiband spectrum access impose a number of challenges yet to overcome. This paper provides an in-depth analysis on the recent advancements in multiband spectrum sensing techniques, their limitations, and possible future directions to improve them. We study cooperative communications for MB-CRNs to tackle a fundamental limit on diversity and sampling. We also investigate several limits and tradeoffs of various design parameters for MB-CRNs. In addition, we explore the key MB-CRNs performance metrics that differ from the conventional metrics used for single-band based networks.Comment: 22 pages, 13 figures; published in the Proceedings of the IEEE Journal, Special Issue on Future Radio Spectrum Access, March 201

Paraunitary oversampled filter bank design for channel coding

Oversampled filter banks (OSFBs) have been considered for channel coding, since their redundancy can be utilised to permit the detection and correction of channel errors. In this paper, we propose an OSFB-based channel coder for a correlated additive Gaussian noise channel, of which the noise covariance matrix is assumed to be known. Based on a suitable factorisation of this matrix, we develop a design for the decoder's synthesis filter bank in order to minimise the noise power in the decoded signal, subject to admitting perfect reconstruction through paraunitarity of the filter bank. We demonstrate that this approach can lead to a significant reduction of the noise interference by exploiting both the correlation of the channel and the redundancy of the filter banks. Simulation results providing some insight into these mechanisms are provided

New Directions in Subband Coding

Two very different subband coders are described. The first is a modified dynamic bit-allocation-subband coder (D-SBC) designed for variable rate coding situations and easily adaptable to noisy channel environments. It can operate at rates as low as 12 kb/s and still give good quality speech. The second coder is a 16-kb/s waveform coder, based on a combination of subband coding and vector quantization (VQ-SBC). The key feature of this coder is its short coding delay, which makes it suitable for real-time communication networks. The speech quality of both coders has been enhanced by adaptive postfiltering. The coders have been implemented on a single AT&T DSP32 signal processo

Blind identification of acoustic systems and enhancement of reverberant speech

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Acoustic Speaker Localization with Strong Reverberation and Adaptive Feature Filtering with a Bayes RFS Framework

The thesis investigates the challenges of speaker localization in presence of strong reverberation, multi-speaker tracking, and multi-feature multi-speaker state filtering, using sound recordings from microphones. Novel reverberation-robust speaker localization algorithms are derived from the signal and room acoustics models. A multi-speaker tracking filter and a multi-feature multi-speaker state filter are developed based upon the generalized labeled multi-Bernoulli random finite set framework. Experiments and comparative studies have verified and demonstrated the benefits of the proposed methods