J.A. Cadzow

Bio: J.A. Cadzow is an academic researcher from Vanderbilt University. The author has contributed to research in topics: Fourier transform & Approximation theory. The author has an hindex of 1, co-authored 2 publications receiving 150 citations.

Blind deconvolution via cumulant extrema

Abstract: Classical deconvolution is concerned with the task of recovering an excitation signal, given the response of a known time-invariant linear operator to that excitation Deconvolution is discussed along with its more challenging counterpart, blind deconvolution, where no knowledge of the linear operator is assumed This discussion focuses on a class of deconvolution algorithms based on higher-order statistics, and more particularly, cumulants These algorithms offer the potential of superior performance in both the noise free and noisy data cases relative to that achieved by other deconvolution techniques This article provides a tutorial description as well as presenting new results on many of the fundamental higher-order concepts used in deconvolution, with the emphasis on maximizing the deconvolved signal's normalized cumulant

Linear recursive operator's response using the discrete Fourier transform

Abstract: A classic problem in signal processing is that of analysing empirical data in order to extract information contained within that data. The primary goal of this article is to employ the discrete Fourier transform (DFT) techniques for approximating, to a prescribed accuracy, the response of a shift-invariant recursive linear operator to a finite-length excitation. In this development, the required properties of the Fourier transform (FT) are first reviewed with particular attention directed toward the stable implementation of shift-invariant recursive linear operators. This is found to entail the decomposition of such operators into their causal and anticausal component operators. Subsequently, relevant issues related to the approximation of the FT by the DFT are examined. This includes the important properties of the non-uniqueness of mapping between a sequence and a given set of DFT coefficients. In the unit-impulse response approximation, DFT is shown to provide a useful means for approximating the unit-impulse response of a linear recursive operator. This includes making a partial fraction expansion of the operator's frequency-response. The error incurred in using the DFT for effecting the unit-impulse response approximation is then treated. This error analysis involves the introduction of one-sided exponential sequences and their truncated mappings that arise in a natural fashion when employing the DFT. These concepts form the central theme of the article.

Blind system identification

Abstract: Blind system identification (BSI) is a fundamental signal processing technology aimed at retrieving a system's unknown information from its output only. This technology has a wide range of possible applications such as mobile communications, speech reverberation cancellation, and blind image restoration. This paper reviews a number of recently developed concepts and techniques for BSI, which include the concept of blind system identifiability in a deterministic framework, the blind techniques of maximum likelihood and subspace for estimating the system's impulse response, and other techniques for direct estimation of the system input.

Blind Deconvolution of Medical Ultrasound Images: A Parametric Inverse Filtering Approach

Abstract: The problem of reconstruction of ultrasound images by means of blind deconvolution has long been recognized as one of the central problems in medical ultrasound imaging. In this paper, this problem is addressed via proposing a blind deconvolution method which is innovative in several ways. In particular, the method is based on parametric inverse filtering, whose parameters are optimized using two-stage processing. At the first stage, some partial information on the point spread function is recovered. Subsequently, this information is used to explicitly constrain the spectral shape of the inverse filter. From this perspective, the proposed methodology can be viewed as a ldquohybridizationrdquo of two standard strategies in blind deconvolution, which are based on either concurrent or successive estimation of the point spread function and the image of interest. Moreover, evidence is provided that the ldquohybridrdquo approach can outperform the standard ones in a number of important practical cases. Additionally, the present study introduces a different approach to parameterizing the inverse filter. Specifically, we propose to model the inverse transfer function as a member of a principal shift-invariant subspace. It is shown that such a parameterization results in considerably more stable reconstructions as compared to standard parameterization methods. Finally, it is shown how the inverse filters designed in this way can be used to deconvolve the images in a nonblind manner so as to further improve their quality. The usefulness and practicability of all the introduced innovations are proven in a series of both in silico and in vivo experiments. Finally, it is shown that the proposed deconvolution algorithms are capable of improving the resolution of ultrasound images by factors of 2.24 or 6.52 (as judged by the autocorrelation criterion) depending on the type of regularization method used.

Independent component analysis applied on gas sensor array measurement data

Abstract: The performance of gas-sensor array systems is greatly influenced by the pattern recognition scheme applied on the instrument's measurement data. The traditional method of choice is principal component analysis (PCA), aiming for reduction in dimensionality and visualization of multivariate measurement data. PCA, as a second-order statistical tool, performs well in many cases, but lacks the ability to give meaningful representations for non-Gaussian data, which often is a property of gas-sensor array measurement data. If, instead, higher order statistical methods are considered for data analysis, more useful information can be extracted from the data. This paper introduces the higher order statistical method called independent component analysis (ICA) as a novel tool for analysis of gas-sensor array measurement data. A comparison between the performances of PCA and ICA is illustrated both in theory and for two sets of practical measurement data. The described experiments show that ICA is capable of handling sensor drift combined with improved discrimination, dimensionality reduction, and more adequate data representation when compared to PCA.