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The perception of blur due to accommodation failures, insufficient optical correction or imperfect image reproduction is a common source of visual discomfort, usually attributed to an anomalous and annoying distribution of the image spectrum in the spatial frequency domain. In the present paper, this discomfort is related to a loss of the localization accuracy of the observed patterns. It is assumed, as a starting perceptual principle, that the visual system is optimally adapted to pattern localization in a natural environment. Thus, since the best possible accuracy of the image patterns localization is indicated by the positional Fisher Information, it is argued that blur discomfort is strictly related to a loss of this information. Following this concept, a receptive field functional model is adopted to predict the visual discomfort. It is a complex-valued operator, orientation-selective both in the space domain and in the spatial frequency domain. Starting from the case of Gaussian blur, the analysis is extended to a generic type of blur by applying a positional Fisher Information equivalence criterion. Out-of-focus blur and astigmatic blur are presented as significant examples. The validity of the proposed model is verified by comparing its predictions with subjective ratings. The model fits linearly with the experiments reported in independent databases, based on different protocols and settings.

Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an essential task in sonar, radar, acoustics, biomedical and multimedia applications. Many state of the art wide-band DOA estimators coherently process frequency binned array outputs by approximate Maximum Likelihood, Weighted Subspace Fitting or focusing techniques. This paper shows that bin signals obtained by filter-bank approaches do not obey the finite rank narrow-band array model, because spectral leakage and the change of the array response with frequency within the bin create \emph{ghost sources} dependent on the particular realization of the source process. Therefore, existing DOA estimators based on binning cannot claim consistency even with the perfect knowledge of the array response. In this work, a more realistic array model with a finite length of the sensor impulse responses is assumed, which still has finite rank under a space-time formulation. It is shown that signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant eigenvectors of the wide-band space-time sensor cross-correlation matrix. A novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order to recover consistency. The number of sources active at each frequency are estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can be fed to any subspace fitting DOA estimator at single or multiple frequencies. Simulations confirm that the new technique clearly outperforms binning approaches at sufficiently high signal to noise ratio, when model mismatches exceed the noise floor., Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans. on Signal Processing on 12 February 1918. @IEEE2018

In this paper, a novel Full Reference method is proposed for image quality assessment, using the combination of two separate metrics to measure the perceptually distinct impact of detail losses and of spurious details. To this purpose, the gradient of the impaired image is locally decomposed as a predicted version of the original gradient, plus a gradient residual. It is assumed that the detail attenuation identifies the detail loss, whereas the gradient residuals describe the spurious details. It turns out that the perceptual impact of detail losses is roughly linear with the loss of the positional Fisher information, while the perceptual impact of the spurious details is roughly proportional to a logarithmic measure of the signal to residual ratio. The affine combination of these two metrics forms a new index strongly correlated with the empirical Differential Mean Opinion Score (DMOS) for a significant class of image impairments, as verified for three independent popular databases. The method allowed alignment and merging of DMOS data coming from these different databases to a common DMOS scale by affine transformations. Unexpectedly, the DMOS scale setting is possible by the analysis of a single image affected by additive noise., Comment: 15 pages, 9 figures. Copyright notice: The paper has been accepted for publication on the IEEE Trans. on Image Processing on 19/09/2017 and the copyright has been transferred to the IEEE

A method for full-reference visual quality assessment based on the 2-D combination of two diverse metrics is described. The first metric is a measure of structural information loss based on the Fisher information about the position of the structures in the observed images. The second metric acts as a categorical indicator of the type of distortion that images underwent. These two metrics constitute the inner state of a virtual cognitive model, viewed as a system whose output is the automatic visual quality estimate. The use of a 2-D metric fills the intrinsic incompleteness of methods based on a single metric while providing consistent response across different image impairment factors and blind distortion classification capability with a modest computational overhead. The high accuracy and robustness of the method are demonstrated through cross-validation experiments.

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.

A dictionary of complex waveforms suited for multiresolution analysis and individually steerable by multiplication by a complex factor is presented. It is based on circular harmonic wavelets (CHW) and is useful for pattern analysis under rotations. The main theoretical aspects of CHWs are illustrated, and an example of application to motion estimation is provided.

When the angle covered by the target as seen by the sensor is sufficiently narrow, the ISAR imaging technique can be viewed as the tomographic reconstruction process of a synthetic image, which maps on space coordinates the energy backscattered from the target along different observation lines. As an alternative to the Fourier slice based techniques, in this paper a map reconstruction method from its two-dimensional (2-D) Laguerre Gauss (LG) expansion is presented. The LG expansion was already used for efficiently analyzing the orientation and the cross profile of linear patterns in images within a Maximum Likelihood approach. In particular, LG basis functions and expansion coefficients rotate by a simple phase shift, proportional to the rotation angle and the circular harmonic order. In addition, the LG expansion is linearly related to the 2-D Hermite Gauss (2-D HG) expansion, which allows for efficient numerical realizations and a compact model of the returns of Ultra Wide Band (UWB) waveforms, naturally suited for this high resolution scheme. The LG or the 2-D HG truncated expansion of the map is finally computed by the linear Least Squares interpolation of a set of matched filter outputs and used for reconstructing the backscattering map. Several system aspects of the LG ISAR method are discussed and computer experiments with tight concentrations of point scatterers illuminated by UWB pulse trains are presented.

The nice relationship existing among the Hermite-Gauss and the Laguerre-Gauss image expansions, whose basis functions span the same signal space, is investigated. As a result, a novel efficient method for Cartesian to polar coordinate inter-conversion, especially suited for dedicated hardware realization, is proposed. Applications to local image rotation, based on the simple steerability of the Laguerre-Gauss expansion, and to local image analysis, based on Gaussian derivatives, are considered in detail. A possible fixed-point realization of the proposed inter-conversion scheme is discussed.

A method for measuring the orientation of linear (1-D) patterns, based on a local expansion with Laguerre-Gauss circular harmonic (LG-CH) functions, is presented. It lies on the property that the polar separable LG-CH functions span the same space as the 2-D Cartesian separable Hermite-Gauss (2-D HG) functions. Exploiting the simple steerability of the LG-CH functions and the peculiar block-linear relationship among the two expansion coefficients sets, maximum likelihood (ML) estimates of orientation and cross section parameters of 1-D patterns are obtained projecting them in a proper subspace of the 2-D HG family. It is shown in this paper that the conditional ML solution, derived by elimination of the cross section parameters, surprisingly yields the same asymptotic accuracy as the ML solution for known cross section parameters. The accuracy of the conditional ML estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials. A thorough proof of the key relationship between the LG-CH and the 2-D HG expansions is also provided.

A twin stage texture synthesis-by-analysis method is presented. It aims to approximate first- and second-order distributions of the texture, accordingly to the Julesz conjecture. In the first stage, the binary textural behavior of a given prototype is represented by means of a hard-limited Gaussian process. In the second stage, the texture is synthesized by passing the binary hard-limited Gaussian process through a linear filter followed by a zero memory histogram equalizer.

In this contribution a procedure of eye detection and localization for biometric applications is presented. It is essentially based on the calculus of two polar moments whose values are employed for detection and localization of pupils. The polar moments are calculated using a bank of mono-dimensional Hermite filters whose outputs can be easily converted to give the local expansion of the analyzed image in the Gauss Laguerre polar separable family of functions.

The technique of template matching in the log-polar visibility (magnitude of Fourier transform in the logarithmic radius and azimuth plane) is proposed as a promising tool for many problems of isolated object recognition irrespective of its position, scale, and rotation. The properties of the log-polar visibility suggests the use of partial information to implement some forms of "reduced template matching". These techniques imply substantial reduction in the computational cost.

The problem of frequency and frequency rate estimation from interrupted observations is addressed. The intuitive fact that the accuracy can be greatly improved by using separate observation intervals is quantitatively discussed. Cramer-Rao bounds and ambiguity functions are given and structures of maximum likelihood receivers are considered.

Usual approaches to localization, i.e., joint estimation of position, orientation and scale of a bidimensional pattern employ suboptimum techniques based on invariant signatures, which allow for position estimation independent of scale and orientation. In this paper a Maximum Likelihood method for pattern localization working in the Gauss-Laguerre Transform (GLT) domain is presented. The GLT is based on an orthogonal family of Circular Harmonic Functions with specific radial profiles, which permits optimum joint estimation of position and scale/rotation parameters looking at the maxima of a "Gauss-Laguerre Likelihood Map." The Fisher information matrix for any given pattern is given and the theoretical asymptotic accuracy of the parameter estimates is calculated through the Cramer Rao Lower Bound. Application of the ML estimation method is discussed and an example is provided.

The optimum design of blind fractionally spaced equalizers is addressed within the framework of a Bayesian approach. The resulting iterative Bussgang-like equalizer design incorporates constraints on the overall channel-equalizer response in order to meet the Nyquist characteristic (raised cosine). The experienced convergence robustness also results in increased accuracy.

The problem of recognizing and locating isolated objects from their images is addressed, and a complete procedure is described. The technique is based on a template matching in the log-polar amplitude spectrum domain and in the space domain. This makes it possible to take properly into account both spectral features and spatial details and to measure with accuracy the scale factor, the orientation, and the absolute position of the object. To reduce the computational burden, pairs of tomographic projections are used in both domains. As an example, the double tomographic method is applied to the classical problem of the automatic reading of printed characters, with the additional specification of unknown size and orientation, and shows good results. >