Preface Through many centuries physics has been one of the most fruitful sources of inspiration for mathematics. As a consequence, mathematics has become an economic language providing a few basic principles which allow to explain a large variety of physical phenomena. Many of them are described in terms of partial diierential equations (PDEs). In recent years, however, mathematics also has been stimulated by other novel elds such as image processing. Goals like image segmentation, multiscale image representation, or image restoration cause a lot of challenging mathematical questions. Nevertheless, these problems frequently have been tackled with a pool of heuristical recipes. Since the treatment of digital images requires very much computing power, these methods had to be fairly simple. With the tremendous advances in computer technology in the last decade, it has become possible to apply more sophisticated techniques such as PDE-based methods which have been inspired by physical processes. Among these techniques, parabolic PDEs have found a lot of attention for smoothing and restoration purposes, see e.g. 113]. To restore images these equations frequently arise from gradient descent methods applied to variational problems. Image smoothing by parabolic PDEs is closely related to the scale-space concept where one embeds the original image into a family of subsequently simpler , more global representations of it. This idea plays a fundamental role for extracting semantically important information. The pioneering work of Alvarez, Guichard, Lions and Morel 11] has demonstrated that all scale-spaces fulllling a few fairly natural axioms are governed by parabolic PDEs with the original image as initial condition. Within this framework, two classes can be justiied in a rigorous way as scale-spaces: the linear diiusion equation with constant dif-fusivity and nonlinear so-called morphological PDEs. All these methods satisfy a monotony axiom as smoothing requirement which states that, if one image is brighter than another, then this order is preserved during the entire scale-space evolution. An interesting class of parabolic equations which pursue both scale-space and restoration intentions is given by nonlinear diiusion lters. Methods of this type have been proposed for the rst time by Perona and Malik in 1987 190]. In v vi PREFACE order to smooth the image and to simultaneously enhance semantically important features such as edges, they apply a diiusion process whose diiusivity is steered by local image properties. These lters are diicult to analyse mathematically , as they may act locally like a backward diiusion process. …

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Anisotropic diffusion in image processing

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

Underwater wireless information transfer is of great interest to the military, industry, and the scientific community, as it plays an important role in tactical surveillance, pollution monitoring, oil control and maintenance, offshore explorations, climate change monitoring, and oceanography research. In order to facilitate all these activities, there is an increase in the number of unmanned vehicles or devices deployed underwater, which require high bandwidth and high capacity for information transfer underwater. Although tremendous progress has been made in the field of acoustic communication underwater, however, it is limited by bandwidth. All this has led to the proliferation of underwater optical wireless communication (UOWC), as it provides higher data rates than the traditional acoustic communication systems with significantly lower power consumption and simpler computational complexities for short-range wireless links. UOWC has many potential applications ranging from deep oceans to coastal waters. However, the biggest challenge for underwater wireless communication originates from the fundamental characteristics of ocean or sea water; addressing these challenges requires a thorough understanding of complex physio-chemical biological systems. In this paper, the main focus is to understand the feasibility and the reliability of high data rate underwater optical links due to various propagation phenomena that impact the performance of the system. This paper provides an exhaustive overview of recent advances in UOWC. Channel characterization, modulation schemes, coding techniques, and various sources of noise which are specific to UOWC are discussed. This paper not only provides exhaustive research in underwater optical communication but also aims to provide the development of new ideas that would help in the growth of future underwater communication. A hybrid approach to an acousto-optic communication system is presented that complements the existing acoustic system, resulting in high data rates, low latency, and an energy-efficient system.

Underwater Optical Wireless Communication

Underwater wireless communications refer to data transmission in unguided water environment through wireless carriers, i.e., radio-frequency (RF) wave, acoustic wave, and optical wave. In comparison to RF and acoustic counterparts, underwater optical wireless communication (UOWC) can provide a much higher transmission bandwidth and much higher data rate. Therefore, we focus, in this paper, on the UOWC that employs optical wave as the transmission carrier. In recent years, many potential applications of UOWC systems have been proposed for environmental monitoring, offshore exploration, disaster precaution, and military operations. However, UOWC systems also suffer from severe absorption and scattering introduced by underwater channels. In order to overcome these technical barriers, several new system design approaches, which are different from the conventional terrestrial free-space optical communication, have been explored in recent years. We provide a comprehensive and exhaustive survey of the state-of-the-art UOWC research in three aspects: 1) channel characterization; 2) modulation; and 3) coding techniques, together with the practical implementations of UOWC.

A Survey of Underwater Optical Wireless Communications

In this paper, we focus on techniques for vector-valued image regularization, based on variational methods and PDE. Starting from the study of PDE-based formalisms previously proposed in the literature for the regularization of scalar and vector-valued data, we propose a unifying expression that gathers the majority of these previous frameworks into a single generic anisotropic diffusion equation. On one hand, the resulting expression provides a simple interpretation of the regularization process in terms of local filtering with spatially adaptive Gaussian kernels. On the other hand, it naturally disassembles any regularization scheme into the smoothing process itself and the underlying geometry that drives the smoothing. Thus, we can easily specialize our generic expression into different regularization PDE that fulfill desired smoothing behaviors, depending on the considered application: image restoration, inpainting, magnification, flow visualization, etc. Specific numerical schemes are also proposed, allowing us to implement our regularization framework with accuracy by taking the local filtering properties of the proposed equations into account. Finally, we illustrate the wide range of applications handled by our selected anisotropic diffusion equations with application results on color images.

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Vector-valued image regularization with PDEs: a common framework for different applications

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

We consider in this paper channel modeling for underwater optical channels. In particular, we focus on the channel impulse response and quantify the channel time dispersion under different conditions of water type, link distance, and transmitter/receiver parameters. We use the Monte Carlo approach to simulate the trajectories of emitted photons propagating in water towards the receiver. We show that in most practical cases, the time dispersion is negligible and does not induce any inter-symbol interference on the received symbols. Our results can be used to appropriately set different system design parameters.

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Channel modeling for underwater optical communication

Because of its ability of providing very high data transmission rates over distances up to several tens of meters, underwater wireless optical communication (UWOC) has attracted considerable interest during the past few years. The underwater channel is a challenging environment, especially because of its high attenuation. The difficulty of precise localization underwater also leads to unavoidable link misalignments that can have an important impact on the link availability and otherwise on the quality of signal transmission. In this paper, after a review of the recent research works on UWOC and the available commercialized systems, we present the performance study of a typical UWOC system under some simplifying assumptions for system modeling. We also address the open issues and the challenges that we are faced with in practice.

Underwater wireless optical communication; recent advances and remaining challenges

The main goal of the UNION ESPRIT Basic Research Action is to develop methods for increasing the autonomy and intelligence of underwater remotely operated vehicles (ROVs). The project focuses mainly on the development of coordinated control and sensing strategies for combined manipulator and vehicle systems. Both fundamental theories and methods for the design of these heterogeneous systems are investigated. A complex canonical mission in the field of offshore inspection maintenance and repair tasks was chosen as an integration guideline of all the results.

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UNION: underwater intelligent operation and navigation

We investigate in this paper the effect of transmitter-receiver misalignment on an underwater point-to-point optical link. Such link misalignments are unavoidable in practice, especially when considering a communication with a moving platform. We take into account practical system parameters including the transmitter beam parameters and the limited receiver field-of-view, and also discuss the choice of receiver optics' parameters. The results we present are based on Monte Carlo simulations which take into consideration the beam absorption and scattering in water. Furthermore, we present some experimental results on the effect of link misalignment using a set-up that we have developed in a pool of 3.5m length. The results presented in this work give insight into practical limitations of establishing such underwater links.

Vincent Rigaud

Papers

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

Channel modeling for underwater optical communication

Underwater wireless optical communication; recent advances and remaining challenges

UNION: underwater intelligent operation and navigation

Misalignment considerations in point-to-point underwater wireless optical links