Caroline Fossati

Denoising of Hyperspectral Images Using the PARAFAC Model and Statistical Performance Analysis

Denoising is an important preprocessing step to further analyze a hyperspectral image (HSI). The common denoising methods, such as 2-D (two dimensions) filter, actually rearrange data from 3-D to 2-D and ignore the spectral relationships among different bands of the image. Tensor decomposition method has been adapted to denoise HSIs, for instance Tucker3 (three-mode factor analysis) model. However, this model has problems in uniqueness of decomposition and in estimation of multiple ranks. In this paper, to overcome these problems, we exploit a powerful multilinear algebra model, named parallel factor analysis (PARAFAC), and the number of estimated rank is reduced to one. Assumed that HSI is disturbed by white Gaussian noise, the optimal rank of PARAFAC is estimated according to that the covariance matrix of the n-mode unfolding matrix of the removed noise should be approach to a scalar matrix. Then, the denoising results by PARAFAC decomposition are presented and compared with those obtained by Tucker3 model and 2-D filters. To further verify the denoising performance of PARAFAC decomposition, Cramer-Rao lower bound (CRLB) of denoising is deduced theoretically for the first time, and the experiment results show that the PARAFAC model is a preferable denoising method since the variance of the HSI denoised by it is closer to the CRLB than by other considered methods.

The finite element method as applied to the diffraction by an anisotropic grating.

The main goal of the method proposed in this paper is the numerical study of various kinds of anisotropic gratings deposited on isotropic substrates, without any constraint upon the diffractive pattern geometry or electromagnetic properties. To that end we propose a new FEM (Finite Element Method) formulation which rigorously deals with each infinite issue inherent to grating problems. As an example, 2D numerical experiments are presented in the cases of the diffraction of a plane wave by an anisotropic aragonite grating on silica substrate (for the two polarization cases and at normal or oblique incidence). We emphasize the interesting property that the diffracted field is non symmetric in a geometrically symmetric configuration.

Comparison of shape descriptors for hand posture recognition in video

Hand posture recognition remains a challenging task for in-line systems working directly in the video stream. In this work, we compare several shape descriptors, with the objective of finding a good compromise between accuracy of recognition and computation load for a real-time application. Experiments are run on two families of contour-based Fourier descriptors and two sets of region-based moments, all of them are invariant to translation, rotation and scale changes of hands. These methods are independent of the camera view point. Systematic tests are performed on the Triesch benchmark database and on our own large database, which includes more realistic conditions. Temporal filtering and a method for unknown posture detection are considered to improve posture recognition results in case of video stream processing.

Integrated photothermal microscope and laser damage test facility for in-situ investigation of nanodefect induced damage.

An integrated setup allowing high resolution photothermal microscopy and laser damage measurements at the same wavelength has been implemented. The microscope is based on photothermal deflection of a transmitted probe beam : the probe beam (633 nm wavelength) and the CW pump beam (1.06 microm wavelength) are collinear and focused through the same objective. In-situ laser irradiation tests are performed thanks to a pulsed beam (1.06 microm wavelength and 6 nanosecond pulse). We describe this new facility and show that it is well adapted to the detection of sub-micronic absorbing defects, that, once located, can be precisely aimed and irradiated. Photothermal mappings are performed before and after shot, on metallic inclusions in dielectric. Results obtained on gold inclusions of about 600 nm in diameter embedded in silica are presented.

Multiwavelength imaging of defects in ultraviolet optical materials

Laser-induced damage in bare glass substrates and thin films has long been widely acknowledged as a localized phenomenon associated with the presence of micrometer and submicrometer scale defects. The scanning of both optical absorption and scattering allows us to discriminate between absorbing and nonabsorbing defects and can give specific information about the origin of the defects. We investigate the spectral properties of defects in thin films and fused-silica surfaces. Absorbing and scattering defects are studied at different wavelengths in the ultraviolet, visible, and infrared ranges. Absorbing defects are shown to be highly wavelength dependent, whereas we have observed significant correlation between scattering defects.

Hand posture classification by means of a new contour signature

This paper deals with hand posture recognition. Thanks to an adequate setup, we afford a database of hand photographs. We propose a novel contour signature, obtained by transforming the image content into several signals. The proposed signature is invariant to translation, rotation, and scaling. It can be used for posture classification purposes. We generate this signature out of photographs of hands: experiments show that the proposed signature provides good recognition results, compared to Hu moments and Fourier descriptors.

Statistical-based linear vessel structure detection in medical images

Linear structures such as blood vessels in medical images are important features for computer-aided diagnosis and follow-up of many diseases. In this letter a new tracking-based segmentation method is proposed to detect blood vessels in retinal angiorams. Bayesian segmentation with the Maximum a posteriori (MAP) Probability criterion is used for that purpose. First promising results are presented and discussed.

Bearing and range estimation algorithm for buried object in underwater acoustics

A new algorithm which associates (Multiple Signal Classification) MUSIC with acoustic scattering model for bearing and range estimation is proposed. This algorithm takes into account the reflection and the refraction of wave in the interface of water-sediment in underwater acoustics. A new directional vector, which contains the Direction-Of-Arrival (DOA) of objects and objects-sensors distances, is used inMUSIC algorithm instead of classical model. The influence of the depth of buried objects is discussed. Finally, the numerical results are given in the case of buried cylindrical shells.

Fast subspace-based source localization methods

Source localization is based on the spectral matrix algebraic properties. Propagator, and Ermolaev-Gershman (EG) noneigenvector algorithms exhibit a low computational load. Propagator is based on spectral matrix partitioning. EG algorithm obtains an approximation of noise subspace using an adjustable power parameter of the spectral matrix and choosing a threshold value. In this paper, we aim at demonstrating the usefulness of QR and LU factorizations of the spectral matrix to improve these methods. Experiments show that the modified propagator and EG algorithms based on factorized spectral matrix lead to better localization results, compared to the existing methods.

Multidimensional Signal Processing and Applications

In our daily lives and almost unconsciously, we deal with multidimensional data. From color images converted to the luminance and chrominance format to magnetic resonance images commonly acquired for health purposes, from different fashions to write an alphabet to array processing signals underlying any telecommunication system, we deal with multidimensional data. In this special issue, we tried to show the variety of the topics which are currently investigated with multidimensional signal processing tools. The mathematical tools presented in this issue are as diverse as adaptive detectors, wavelet processing, principal component analysis, and improved classical image processing tools such as histogram equalization. In the array processing paradigm, a two-dimensional matrix containing the data depends on the polarization properties of the sources, their number, and the number of sensors in the receiving antenna. Hence the interest of a multidimensional representation, including a polarization variable with two or three possible values, and a real and a complex part for the source amplitudes. In the image processing paradigm, data are as various as magnetic resonance or color images, whose representation can be transferred from the RGB (red green blue) format to other spaces emphasizing for instance the luminance or the chrominance. It is shown how magnetic resonance brain images are classified with support vector machine. To avoid problems related to high dimensionality, which is current in big data processing, adequate features are extracted from the data by discrete wavelet transform and principal component analysis. Color spaces, which are useful for skin detection, for instance, are also further investigated: whatever the representation space is, a color image is a third order tensor, in other words, a three-dimensional data. It is shown how to detect image splicing with the help of merged features in the chrominance space: the relationships between pixels in a neighborhood are studied with a Markov process and the extraction of DCT features from the chrominance channel. Then, with the help of new color spaces, it is shown how evolved versions of neural networks called extreme learning machines can fuse multiple information such as color and local spatial information from face images. The “multi” aspect can also appear in the image processing paradigm when multiple images are obtained from several parameters. In images provided by synthetic aperture radar exploited for flood detection, contrast enhancement is achieved by an adjustable histogram equalization technique. For such an application where the visual aspect of the results are much important much, a color image, that is, a multidimensional signal, can be built from several two-dimensional result images, to get an informative map, where the color informs on the nature of the imaged scene, flooded or not, for instance. Starting from images, a set of multidimensional data is extracted from Serbian texts: the Serbian alphabet, made of 30 letters, can be expressed in a Latin or in a Cyrillic fashion. All letters can be classified into four sets. By studying the frequencies of occurrence of each type of letter in a text, one can deduce that this text is written in the Latin or the Cyrillic fashion. In this application, matrices describing the cooccurrence in the distribution of the four types of letters are built out of any text, to make use of the classical texture features. Adapting the texture features to such a text recognition application, introducing a parameter which is the writing fashion, is a brand new idea. The “multi” aspect can also relate to multiresolution. Histogram of oriented gradients and hue descriptors can be merged to combine information related to the shape of an object and its color. By computing the merged data at several resolution levels, an innovative multidimensional descriptor is obtained. An application considered in this special issue is aircraft characterization and detection of images. In a nutshell, the “multi” representation attracts the interest of researchers from very diverse application fields. Hopefully, this special issue will contribute in diffusing the models and tools of multidimensional signal processing to various application fields. Salah Bourennane Julien Marot Caroline Fossati Ahmed Bouridane Klaus Spinnler