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.

/pdf/a-parametric-texture-model-based-on-joint-statistics-of-2p5nbgtfy6.pdf

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.

/pdf/optical-coherence-tomography-principles-and-applications-17y32cabbm.pdf

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

At present, system design usually assumes the Kolmogorov model of refractive index fluctuation spectra in the
atmosphere. However, experimental data indicates that in the atmospheric boundary layer and at higher altitudes the
turbulence can be different from Kolmogorov's type.
In optical communications, analytical models of mean irradiance and scintillation index have been developed for a
traditional Kolmogorov spectrum and must be revised for non-Kolmogorov turbulence.
The image quality (resolution, MTF, etc.) is essentially dependent on the properties of turbulent media. Turbulence MTF
must be generalized to include non-Kolmogorov statistics. The change in fluctuation correlations of the refractive index
can lead to a considerable change in both the MTF form and the resolution value.
In this work, on the basis of measurements and model calculations, the influence of non-Kolmogorov turbulence on
imaging and communications through the atmosphere is estimated for different scenarios of vertical and slant-path
propagation. The atmospheric model of an arbitrary (non-Kolmogorov) spectrum is applied to estimate the statistical
quantities associated with optical communication links (e.g., scintillation and fading statistics) and imaging system.
Implications can be significant for optical communication, imaging through the atmosphere, and remote sensing.

Imaging and communications through non-Kolmogorov turbulence

Aerosol blur, often referred to as the adjacency effect, is well-established as the primary and perhaps only source of atmospheric blur in remote sensing imaging from satellites. However, much of the propagation community considers turbulence blur only in interpreting experiments, and then notes discrepancies with turbulence theory without considering how aerosol blur may have affected their experiments, Because of the complexities of atmospheric and meteorological processes a broad system engineering approach is called for, which includes aerosols, turbulence, absorption, and any other atmospheric effects. In general, turbulence is most significant at low elevations up to a few meters above earth's surface, and aerosol blur is most significant at higher elevations, especially if optical depth is on the order of unity or more.

Causes of blur in imaging through the atmosphere: a system engineering approach to imaging

Aerosol blur, often referred to as the adjacency effect, is well-established as the primary and perhaps only source of atmospheric blur in remote sensing imaging from satellites. However, much of the propagation community considers turbulence blur only in interpreting experiments. Because of the complexities of atmospheric and meteorological processes a broad system engineering approach is called for, which includes aerosols, turbulence, absorption, and other atmospheric effects. In general, turbulence is most significant at low elevations up to a few meters above earth's surface, and aerosol blur is most significant at higher elevations, especially if optical depth is on the order of unity or more. However, turbulence and aerosol effects increase in the stratosphere.

Causes of atmospheric blur in remote sensing: a system engineering approach to imaging

Low temporal frequency vibrations involve random image degradation depending on the instant of exposure. Exact restoration requires calculating a specific filter unique to each vibrated image. In order to calculate the restoration filter for each image the specific degradation function is needed. Therefore, the instant of exposure has to be measured or estimated by some other means. In this work a general restoration filter for a single vibrated image is developed. The filter is independent of the instant of exposure. Assuming that receiving each image from a vibrated image ensemble is equally likely, the filter is designed to give best performance averaged over the ensemble. Even though when applying the new filter to any vibrated image the restoration achieved is slightly poorer than with an exact filter based on the specific motion function, the new filter has the advantage of simplicity. Since the instant of exposure is not needed a new appropriate filter does not have to be calculated for each exposure, the proposed filter is more practical and suitable for real time restoration.

General restoration filter for vibrated image restoration

The recently introduced non-local means (NLM) image denoising technique broke the traditional
paradigm according to which image pixels are processed by their surroundings. Non-local means technique
was demonstrated to outperform state-of-the art denoising techniques when applied to images in the visible.
This technique is even more powerful when applied to low contrast images, which makes it tractable for
denoising infrared (IR) images. In this work we investigate the performance of NLM applied to infrared
images. We also present a new technique designed to speed-up the NLM filtering process. The main
drawback of the NLM is the large computational time required by the process of searching similar patches.
Several techniques were developed during the last years to reduce the computational burden. Here we present
a new techniques designed to reduce computational cost and sustain optimal filtering results of NLM
technique. We show that the new technique, which we call Multi-Resolution Search NLM (MRS-NLM),
reduces significantly the computational cost of the filtering process and we present a study of its performance
on IR images.

/pdf/infrared-image-denoising-by-nonlocal-means-filtering-4pg2zwundb.pdf

Norman S. Kopeika

Papers

Imaging and communications through non-Kolmogorov turbulence

Causes of blur in imaging through the atmosphere: a system engineering approach to imaging

Causes of atmospheric blur in remote sensing: a system engineering approach to imaging

General restoration filter for vibrated image restoration

Infrared image denoising by nonlocal means filtering