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.

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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

The recently developed atmospheric Wiener filter, which corrects for turbulence and aerosol blur and path radiance simultaneously, is implemented in digital restoration of AVHRR imagery over the five wavelength bands of the satellite instrumentation. Restoration is most impressive for higher optical depth situations, with improvement with regard to both smallness of size of resolvable detail and contrast Turbulence modulation transfer function (MTF) is calculated from meteorological data. Aerosol MTF is calculated from optical depth, measured with a sun-photometer. The product of the two yields atmospheric MiT which is implemented in the atmospheric Wiener filter. Image restorations with accompanying atmospheric MTF curves are presented. However, restoration results using a simple inverse MTF filter were quite similar. This indicates the satellite images were characterized by very low noise and that turbulence jitter was very limited which, in turn, indicates that the twbulencc MTFs integrated upwards over the path length were small compared to aerosol MTFs.

Restoration of satellite images based on atmospheric MTF

It is suggested here that the lack of total image correction that is typical in adaptive optics (AO) imaging can be attributed in part to blur derived from small-angle scatter of light by aerosols, known also as the adjacency effect, especially as it is a well-established fact that such atmospheric blur is dominant in satellite imagery and the shape of the modulation transfer function after AO correction is strikingly similar to the unique shape of the aerosol modulation transfer function. Further investigation of AO systems to confirm this would aid in and improve image restoration.

Myopic Deconvolution of Adaptive Optics Images by use of Object and Point-Spread Function Power Spectra: Comment.

A correction to the definition of the atmospheric coherence diameter is suggested here. The basis of this new approach is the existence of an aerosol MTF which is often the dominant ingredient of the atmospheric MTF. As defined by Fried about 25 years ago, atmospheric MTFwas related to turbulence MTh only. In the case of a Gaussian approximation of the aerosol MTF,an analytical expression is derived for the aerosol-caused coherence diameter. This parameter is related to the aerosol MTF's cutoff frequency, and to its asymptote at high spatial frequencies which was recently shown to be higher than the atmospheric transmittance. Qualitative validationof the theory is presented, based on measured MTFs in the open atmosphere. Overall atmospheric coherence diameter is generally the smaller between the turbulence and aerosol coherence diameters. INTRODUCTION The concept of atmospheric coherence diameter was first introduced by Fried over 25 years ago1'2, and is a very important parameter with which to characterise resolution through a turbulentatmosphere. Recent investigations of the subject 36 have shown significant effects of small angle

Effects of aerosol forward scatter on atmospheric coherence diameter: theory and validation

Low noise images are contract-limited, and image restoration techniques can improve resolution significantly. However, as noise level increases, resolution improvements via image processing become more limited because image restoration increases noise. This research attempts to construct a reliable quantitative means of characterizing the perceptual difference between target and background. A method is suggested for evaluating the extent to which it is possible to discriminate an object which has merged with its surroundings, in noise-limited and contrast limited images, i.e., how hard it would be for an observer to recognize the object against various backgrounds as a function of noise level. The suggested model will be a first order model to begin with, using a regular bar-chart with additive uncorrelated Gaussian noise degraded by standard atmospheric blurring filters. The second phase will comprise a model dealing with higher-order images. This computational model relates the detectability or distinctness of the object to measurable parameters. It also must characterize human perceptual response, i.e. the model must develop metrics which are highly correlated to the ease or difficulty which the human observer experiences in discerning the target from its background. This requirement can be fulfilled only by conducting psychophysical experiments quantitatively comparing the perceptual evaluations of the observers with the results of the mathematical model.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Contrast vs noise effects on image quality

Vibrations are often a major cause of image degradation in airborne ad terrestrial reconnaissance, astronomy, robotics, machine vision and computer vision systems. In the case of low-frequency vibration (the exposure time is shorter than the vibration period time) the camera motion during the exposure is random, depending on the vibration parameters (amplitude and frequency) and on the instant of the exposure time. Therefore, the random motion causes a random image blur. Knowledge of the exact motion is practical for calculation of motion optical transfer function (OTF) which can be used with common image restoration algorithms. The motion can be either measured directly using motion sensors or estimated from a sequence of images. Here, a vibration motion estimation method from a minimal sequence of two images is presented. Motion estimation from only two consecutive images is possible due to the use of information hidden in the image blur. The process is carried out in the frequency domain using a new analytical motion OTF calculation method.

Norman S. Kopeika

Papers

Restoration of satellite images based on atmospheric MTF

Myopic Deconvolution of Adaptive Optics Images by use of Object and Point-Spread Function Power Spectra: Comment.

Effects of aerosol forward scatter on atmospheric coherence diameter: theory and validation

Contrast vs noise effects on image quality

Vibrated image restoration from two consecutive images