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

We present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. We develop an efficient algorithm for synthesizing random images subject to these constraints, by iteratively projecting onto the set of images satisfying each constraint, and we use this to test the perceptual validity of the model. In particular, we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set. We also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures.

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A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients

There have been three basic approaches to optical tomography since the early 1980s: diffraction tomography, diffuse optical tomography and optical coherence tomography (OCT). Optical techniques are of particular importance in the medical field, because these techniques promise to be safe and cheap and, in addition, offer a therapeutic potential. Advances in OCT technology have made it possible to apply OCT in a wide variety of applications but medical applications are still dominating. Specific advantages of OCT are its high depth and transversal resolution, the fact, that its depth resolution is decoupled from transverse resolution, high probing depth in scattering media, contact-free and non-invasive operation, and the possibility to create various function dependent image contrasting methods. This report presents the principles of OCT and the state of important OCT applications. OCT synthesises cross-sectional images from a series of laterally adjacent depth-scans. At present OCT is used in three different fields of optical imaging, in macroscopic imaging of structures which can be seen by the naked eye or using weak magnifications, in microscopic imaging using magnifications up to the classical limit of microscopic resolution and in endoscopic imaging, using low and medium magnification. First, OCT techniques, like the reflectometry technique and the dual beam technique were based on time-domain low coherence interferometry depth-scans. Later, Fourier-domain techniques have been developed and led to new imaging schemes. Recently developed parallel OCT schemes eliminate the need for lateral scanning and, therefore, dramatically increase the imaging rate. These schemes use CCD cameras and CMOS detector arrays as photodetectors. Video-rate three-dimensional OCT pictures have been obtained. Modifying interference microscopy techniques has led to high-resolution optical coherence microscopy that achieved sub-micrometre resolution. This report is concluded with a short presentation of important OCT applications. Ophthalmology is, due to the transparent ocular structures, still the main field of OCT application. The first commercial instrument too has been introduced for ophthalmic diagnostics (Carl Zeiss Meditec AG). Advances in using near-infrared light, however, opened the path for OCT imaging in strongly scattering tissues. Today, optical in vivo biopsy is one of the most challenging fields of OCT application. High resolution, high penetration depth, and its potential for functional imaging attribute to OCT an optical biopsy quality, which can be used to assess tissue and cell function and morphology in situ. OCT can already clarify the relevant architectural tissue morphology. For many diseases, however, including cancer in its early stages, higher resolution is necessary. New broad-bandwidth light sources, like photonic crystal fibres and superfluorescent fibre sources, and new contrasting techniques, give access to new sample properties and unmatched sensitivity and resolution.

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Optical coherence tomography - principles and applications

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.

/pdf/survey-on-free-space-optical-communication-a-communication-239v68hfyw.pdf

Survey on Free Space Optical Communication: A Communication Theory Perspective

In free-space optical communication links, atmospheric turbulence causes fluctuations in both the intensity and the phase of the received light signal, impairing link performance. We describe several communication techniques to mitigate turbulence-induced intensity fluctuations, i.e., signal fading. These techniques are applicable in the regime in which the receiver aperture is smaller than the correlation length of fading and the observation interval is shorter than the correlation time of fading. We assume that the receiver has no knowledge of the instantaneous fading state. When the receiver knows only the marginal statistics of the fading, a symbol-by-symbol ML detector can be used to improve detection performance. If the receiver has knowledge of the joint temporal statistics of the fading, maximum-likelihood sequence detection (MLSD) can be employed, yielding a further performance improvement, but at the cost of very high complexity. Spatial diversity reception with multiple receivers can also be used to overcome turbulence-induced fading. We describe the use of ML detection in spatial diversity reception to reduce the diversity gain penalty caused by correlation between the fading at different receivers.

/pdf/free-space-optical-communication-through-atmospheric-48mj86nu81.pdf

Free-space optical communication through atmospheric turbulence channels

Free space optical (FSO) communication technology has become increasingly advanced with capabilities of high speed, high capacity, and low power consumption. However, despite the great potential of FSO, its performance is limited in a turbulent atmosphere. Atmospheric turbulence causes scintillation in the FSO propagated signals, leading to an increase in the bit error rate (BER) performance of the recovered signals at the receiver. In this paper, we demonstrate that the use of deep learning (DL) detection methods could overcome these limitations. We present a new detection method of on-off keying (OOK) modulated signals by using different models of DL over different strength FSO turbulent channels, without the need for prior knowledge of the parameters of the channel. The demonstrated DL decoders improve the performance of the FSO turbulent channel and decrease the power consumption. Moreover, the demonstrated DL models also work faster than maximum likelihood (ML) methods with perfect channel estimation decoders, with even slightly better performance because of the turbulence, thus enabling realization of FSO over turbulent atmospheric channels.

/pdf/deep-learning-for-improving-performance-of-ook-modulation-4mzwspglbg.pdf

Deep Learning for Improving Performance of OOK Modulation Over FSO Turbulent Channels

The incorporation of atmospheric aerosol and turbulence effects into visible, near-infrared, and thermalinfrared target acquisition modeling is considered. We show how the target acquisition probabilities and, conversely, the ranges at which objects can be detected are changed by the inclusion of atmospheric effects. It is assumed that images are contrast limited rather than noise limited, as is indeed the case with most visible, near-infrared, and thermal infrared sensors. For short focal lengths with low angular magnification, atmospheric effects on target acquisition are negligible. However, for longer focal lengths with large angular magnification, resolution is limited by the atmosphere, and this has a strong adverse effect on target acquisition probabilities, times, and ranges. The considerable improvement possible with image correction for atmospheric blur automatically in a fraction of a second is significant for contrast-limited imaging and is also discussed. Knowledge of the atmospheric modulation transfer function is essential to good system design and is also useful in image restoration for any type of target or object. Finally, a new target-transferfunction model is suggested that considers the overall image-spectrum target received by the human visual system rather than only the main harmonic detail as in the Johnson chart model. [ J.
	 Johnson
	 
	, in Proceedings of Seminar on Direct-Viewing Electro-Optical Aids to Night Vision ( IDA, Alexandria, Va., 1966), p. 177.]

Target acquisition modeling for contrast-limited imaging: effects of atmospheric blur and image restoration

A method and apparatus to restore images degraded by motion or vibration as characterized by the measurement of the relative motion between the object and the imaging device, calculation of the Optical Transfer Function (OTF) from the Line Spread Function (LSF), and applying a restoration filter M according to the following rule ##EQU1## where H is the image motion OTF, C is the discrete Laplacian operator which is used to minimize the error and γ is the convergence parameter of an iterative algorithm.

Method and apparatus for the restoration of images degraded by mechanical vibrations

A practical instrumentation-based atmospheric aerosol MTF which is a modification of the classical aerosol MTF theory is proposed. The approach based on radiative transfer theory takes into account the effect of finite field-of-view, finite dynamic sensitivity, and finite spatial bandwidth of every existing imaging system. The asymptote value of the measured aerosol MTF approaches at high spatial frequencies is found to be significantly higher than the theoretical prediction of turbid medium transmittance. It is concluded that the aerosol MTF cannot be referred to as constant attenuation, and in many cases it is the dominant part in the actual overall atmospheric MTF. An image resolution-image irradiance relationship can be determined by the system designer through considering field-of-view, instrumentation dynamic range, and spatial frequency bandwidth. It is necessary to choose between imaging of faint and bright objects at the expense of image quality, or imaging of either faint or bright objects with improved image quality.

Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol MTF

A new approach to studying the effects of absorption by aerosols and molecular particulates of electromagnetic radiation is presented. In contradiction to the conventional concept that absorption gives rise to constant attenuation, it is shown here that the particulate-absorbed irradiance is spatial frequency dependent. An analytically corrected model of the aerosol modulation transfer function and the aerosol mutual coherence function is presented. An important application of this model is in thermal imaging, in which particulate-absorption effects are very significant.

Norman S. Kopeika

Papers

Deep Learning for Improving Performance of OOK Modulation Over FSO Turbulent Channels

Target acquisition modeling for contrast-limited imaging: effects of atmospheric blur and image restoration

Method and apparatus for the restoration of images degraded by mechanical vibrations

Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol MTF

Effects of absorption on image quality through a particulate medium