Gianpiero Panci

Multichannel blind image deconvolution using the Bussgang algorithm: spatial and multiresolution approaches

This work extends the Bussgang blind equalization algorithm to the multichannel case with application to image deconvolution problems. We address the restoration of images with poor spatial correlation as well as strongly correlated (natural) images. The spatial nonlinearity employed in the final estimation step of the Bussgang algorithm is developed according to the minimum mean square error criterion in the case of spatially uncorrelated images. For spatially correlated images, the nonlinearity design is rather conducted using a particular wavelet decomposition that, detecting lines, edges, and higher order structures, carries out a task analogous to those of the (preattentive) stage of the human visual system. Experimental results pertaining to restoration of motion blurred text images, out-of-focus spiky images, and blurred natural images are reported.

Robust rotation-invariant texture classification using a model based approach

In this paper, a model based texture classification procedure is presented. The texture is modeled as the output of a linear system driven by a binary image. This latter retains the morphological characteristics of the texture and it is specified by its spatial autocorrelation function (ACF). We show that features extracted from the ACF of the binary excitation suffice to represent the texture for classification purposes. Specifically, we employ a moment invariants based technique to classify the ACF. The resulting proposed classification procedure is thus inherently rotation invariant. Moreover, it is robust with respect to additive noise. Experimental results show that this approach allows obtaining high correct rotation-invariant classification rates while containing the size of the feature space.

Blind phase recovery for QAM communication systems

In this paper, a novel phase estimator that can be employed for both square and cross Quadrature Amplitude Modulation (QAM) based digital transmission is presented. It does not need gain control and requires only the knowledge of the type of the transmitted symbol constellation, i.e., square or cross. It is based on the evaluation of the fourth power of the received data and the measurement of the orientation of the concentration ellipses of the bivariate Gaussian distribution having the same second-order moments. The analytical evaluation of the estimation error as well as of the asymptotic variance is provided. Experimental results outline the good performance of the estimator described here, which is superior to that of well-known phase estimation methods. Finally, it is outlined how the eccentricity of the concentration ellipses can be used to devise a test for detecting the constellation type.

Blind image deblurring driven by nonlinear processing in the edge domain

This work addresses the problem of blind image deblurring, that is, of recovering an original image observed through one or more unknown linear channels and corrupted by additive noise. We resort to an iterative algorithm, belonging to the class of Bussgang algorithms, based on alternating a linear and a nonlinear image estimation stage. In detail, we investigate the design of a novel nonlinear processing acting on the Radon transform of the image edges. This choice is motivated by the fact that the Radon transform of the image edges well describes the structural image features and the effect of blur, thus simplifying the nonlinearity design. The effect of the nonlinear processing is to thin the blurred image edges and to drive the overall blind restoration algorithm to a sharp, focused image. The performance of the algorithm is assessed by experimental results pertaining to restoration of blurred natural images.

Bussgang-zero crossing equalization: an integrated HOS-SOS approach

An integrated higher order statistics (HOS) and second order statistics (SOS) based equalization technique is presented as an extension of the Bussgang equalization algorithm. This extension allows one to simultaneously take account of the statistical knowledge about the data source, as done in the conventional HOS approaches and, in particular, by Bussgang-like equalization algorithms such as super exponential, constant modulus, etc., and the spectral redundancy usually present in pulse-amplitude modulation (PAM) and quadrature-amplitude modulation (QAM) modulated signals, exploited by SOS-based approaches. The technique presented employs a new form of SOS equalization that naturally integrates into the Bussgang scheme. It is based on a zero crossing (ZC) property of the received signal when it is passed through a suitable filter. The novel equalization scheme is presented in a Bayesian estimation framework, after illustration of the general Bussgang paradigm and of the principles of the ZC approach. From simulated experiments, results show that the extended Bussgang-ZC equalizer not only outperforms conventional Bussgang equalizers but is also robust to situations where HOS and SOS approaches individually fail.

Gain-Control-Free Near-Efficient Phase Acquisition for QAM Constellations

This paper introduces a novel, not data aided, phase-offset estimator for quadrature amplitude modulated (QAM) signals. Contrarily to near-efficient existing phase acquisition techniques, this estimator does not require a preliminary gain adjustment stage while its accuracy preserves the slope of Cramer-Rao bound for medium-high signal-to-noise ratio (SNR) ranges, where it typically outperforms existing blind estimators, with significant improvement for dense and cross QAM constellations. Moreover, it needs only a very rough estimate of the SNR. Like other gain-control-free blind phase-offset estimators, it measures the amount of the cyclic shift by which the (four-folded) phase probability density function (pdf) is rotated under an unknown phase-offset. Estimation of the phase-offset-induced cyclic shift is conducted first by measuring the received data phase pdf by a canonical phase histogram procedure, then by estimating the phase-offset-induced cyclic shift through a cyclic cross correlation-based procedure between the measured phase histogram and a reference phase pdf evaluated within the zero phase-offset hypothesis. Actually, the estimation procedure is presented in a generalized version that considers a tomographic projection of the bidimensional (magnitude/phase) pdf of suitable nonlinear transformations of the received data. The tomographic projection performs a magnitude weighing on the pdf, and this, in turn, results in an improved overall estimation accuracy, as shown by theoretical analysis and numerical simulations here performed to assess the estimator performance.

Blind equalization for correlated input symbols: A Bussgang approach

This paper addresses the problem of blind equalization in the case of correlated input symbols, and it shows how the knowledge of the symbol sequence probability distribution can be directly incorporated in a Bussgang blind equalization scheme. Numerical results pertaining to both linear and nonlinear modulation schemes show that a significant improvement in equalization performance is obtained by exploiting the symbol sequence probability distribution using the approach herein described.

Gain-Control-Free Blind Carrier Frequency Offset Acquisition for QAM Constellations

This paper introduces a novel blind frequency offset estimator for quadrature amplitude modulated (QAM) signals. Specifically, after a preliminary frequency compensation, the estimator is based on the ¿/2-folded phase histogram of the received data. Then, the frequency offset estimate is taken as the frequency compensation value that minimizes the mean square error between the phase histogram measured on the received samples and the reference phase probability density function analytically calculated in the case of zero frequency offset. The ¿/2 -folded phase histogram of the received data is here called Constellation Phase Signature, since it definitively characterizes the phase distribution of signal samples belonging to a particular QAM constellation, and it has already been employed to develop a gain-control-free phase estimator that well performs both for square and cross constellations. Also the here described frequency offset estimator has the remarkable property to be gain-control-free and, thus, it can be fruitfully employed in frequency acquisition stages. The asymptotic performance of the estimator has been analytically evaluated and assessed by numerical simulations. Theoretical analysis and numerical results show that the novel frequency offset estimator outperforms state-of-the art estimators in a wide range of signal-to-noise ratio (SNR) values.

Reduced complexity rotation invariant texture classification using a blind deconvolution approach

In this paper, we present a texture classification procedure that makes use of a blind deconvolution approach. Specifically, the texture is modeled as the output of a linear system driven by a binary excitation. We show that features computed from one-dimensional slices extracted from the two-dimensional autocorrelation function (ACF) of the binary excitation allows representing the texture for rotation-invariant classification purposes. The two-dimensional classification problem is thus reconduced to a more simple one-dimensional one, which leads to a significant reduction of the classification procedure computational complexity.

Fractionally spaced Bussgang equalization for correlated input symbols

We address the problem of blind equalization in the case of correlated input symbols. In particular, we focus on the Bussgang blind equalization algorithm, since this allows a simple incorporation of the information associated to the symbol correlation in its computational scheme. Numerical results show that a significant improvement in equalization performance is obtained by exploiting the symbol correlation using the approach described.