There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

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Tensor Decompositions and Applications

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Optical wireless communication (OWC) refers to transmission in unguided propagation media through the use of optical carriers, i.e., visible, infrared (IR), and ultraviolet (UV) bands. In this survey, we focus on outdoor terrestrial OWC links which operate in near IR band. These are widely referred to as free space optical (FSO) communication in the literature. FSO systems are used for high rate communication between two fixed points over distances up to several kilometers. In comparison to radio-frequency (RF) counterparts, FSO links have a very high optical bandwidth available, allowing much higher data rates. They are appealing for a wide range of applications such as metropolitan area network (MAN) extension, local area network (LAN)-to-LAN connectivity, fiber back-up, backhaul for wireless cellular networks, disaster recovery, high definition TV and medical image/video transmission, wireless video surveillance/monitoring, and quantum key distribution among others. Despite the major advantages of FSO technology and variety of its application areas, its widespread use has been hampered by its rather disappointing link reliability particularly in long ranges due to atmospheric turbulence-induced fading and sensitivity to weather conditions. In the last five years or so, there has been a surge of interest in FSO research to address these major technical challenges. Several innovative physical layer concepts, originally introduced in the context of RF systems, such as multiple-input multiple-output communication, cooperative diversity, and adaptive transmission have been recently explored for the design of next generation FSO systems. In this paper, we present an up-to-date survey on FSO communication systems. The first part describes FSO channel models and transmitter/receiver structures. In the second part, we provide details on information theoretical limits of FSO channels and algorithmic-level system design research activities to approach these limits. Specific topics include advances in modulation, channel coding, spatial/cooperative diversity techniques, adaptive transmission, and hybrid RF/FSO systems.

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Survey on Free Space Optical Communication: A Communication Theory Perspective

We consider channel characterization for underwater wireless optical communication (UWOC) systems. We focus on the channel impulse response and, in particular, quantify the channel time dispersion for different water types, link distances, and transmitter/receiver characteristics, taking into account realistic parameters. We use the Monte Carlo approach to simulate the trajectories of emitted photons propagating in water from the transmitter towards the receiver. During their propagation, photons are absorbed or scattered as a result of their interaction with different particles present in water. To model angle scattering, we use the two-term Henyey-Greenstein model in our channel simulator. We show that this model is more accurate than the commonly used Henyey-Greenstein model, especially in pure sea waters. Through the numerical results that we present, we show that, except for highly turbid waters, the channel time dispersion can be neglected when working over moderate distances. In other words, under such conditions, we do not suffer from any inter-symbol interference in the received signal. Lastly, we study the performance of a typical UWOC system in terms of bit-error-rate using the simple on-off-keying modulation. The presented results give insight into the design of UWOC systems.

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Monte-Carlo-based channel characterization for underwater optical communication systems

In hyperspectral image (HSI) analysis, classification requires spectral dimensionality reduction (DR). While common DR methods use linear algebra, we propose a multilinear algebra method to jointly achieve denoising reduction and DR. Multilinear tools consider HSI data as a whole by processing jointly spatial and spectral ways. The lower rank-(K1, K2, K3) tensor approximation [LRTA-(K1, K2, K3)] was successfully applied to denoise multiway data such as color images. First, we demonstrate that the LRTA-(K1, K2, K3) performs well as a denoising preprocessing to improve classification results. Then, we propose a novel method, referred to as LRTAdr-(K1, K2, D3), which performs both spatial lower rank approximation and spectral DR. The classification algorithm Spectral Angle Mapper is applied to the output of the following three DR and noise reduction methods to compare their efficiency: the proposed LRTAdr-(K1, K2, D3), PCAdr, and PCAdr associated with Wiener filtering or soft shrinkage of wavelet transform coefficients.

Denoising and Dimensionality Reduction Using Multilinear Tools for Hyperspectral Images

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.

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

Atmospheric turbulence can cause a significant performance degradation in free-space optical communication systems. It is well known that the effect of turbulence can be reduced by performing aperture averaging and/or employing spatial diversity at the receiver. In this paper, we provide a synthesis on the effectiveness of these techniques under different atmospheric turbulence conditions from a telecommunication point of view. In particular, we quantify the performance improvement in terms of average bit error rate (BER) and outage capacity, which are among important parameters in practice. The efficiency of channel coding and the feasibility of exploiting time diversity in aperture averaging receivers are discussed as well. We also compare single- and multiple-aperture systems from the point of view of fading reduction by considering uncorrelated fading on adjacent apertures for the latter case. We show that when the receiver is background noise limited, the use of multiple apertures is largely preferred to a single large aperture under strong turbulence conditions. A single aperture is likely to be preferred under moderate turbulence conditions, however. When the receiver is thermal noise limited, even under strong turbulence conditions, the use of multiple apertures is interesting only when working at a very low BER. We also provide discussions on several practical issues related to system implementation.

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Fading Reduction by Aperture Averaging and Spatial Diversity in Optical Wireless Systems

A generalized multidimensional Wiener filter for denoising is adapted to hyperspectral images (HSIs). Commonly, multidimensional data filtering is based on data vectorization or matricization. Few new approaches have been proposed to deal with multidimensional data. Multidimensional Wiener filtering (MWF) is one of these techniques. It considers a multidimensional data set as a third-order tensor. It also relies on the separability between a signal subspace and a noise subspace. Using multilinear algebra, MWF needs to flatten the tensor. However, flattening is always orthogonally performed, which may not be adapted to data. In fact, as a Tucker-based filtering, MWF only considers the useful signal subspace. When the signal subspace and the noise subspace are very close, it is difficult to extract all the useful information. This may lead to artifacts and loss of spatial resolution in the restored HSI. Our proposed method estimates the relevant directions of tensor flattening that may not be parallel either to rows or columns. When rearranging data so that flattening can be performed in the estimated directions, the signal subspace dimension is reduced, and the signal-to-noise ratio is improved. We adapt the bidimensional straight-line detection algorithm that estimates the HSI main directions, which are used to flatten the HSI tensor. We also generalize the quadtree partitioning to tensors in order to adapt the filtering to the image discontinuities. Comparative studies with MWF, wavelet thresholding, and channel-by-channel Wiener filtering show that our algorithm provides better performance while restoring impaired HYDICE HSIs.

Salah Bourennane

Papers

Monte-Carlo-based channel characterization for underwater optical communication systems

Denoising and Dimensionality Reduction Using Multilinear Tools for Hyperspectral Images

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

Fading Reduction by Aperture Averaging and Spatial Diversity in Optical Wireless Systems

Noise Removal From Hyperspectral Images by Multidimensional Filtering