Rician Statistics Research Articles

On 1-Laplacian Elliptic Equations Modeling Magnetic Resonance Image Rician Denoising

Modeling magnitude Magnetic Resonance Images (MRI) rician denoising in a Bayesian or generalized Tikhonov framework using Total Variation (TV) leads naturally to the consideration of nonlinear elliptic equations. These involve the so called $1$-Laplacian operator and special care is needed to properly formulate the problem. The rician statistics of the data are introduced through a singular equation with a reaction term defined in terms of modified first order Bessel functions. An existence theory is provided here together with other qualitative properties of the solutions. Remarkably, each positive global minimum of the associated functional is one of such solutions. Moreover, we directly solve this non--smooth non--convex minimization problem using a convergent Proximal Point Algorithm. Numerical results based on synthetic and real MRI demonstrate a better performance of the proposed method when compared to previous TV based models for rician denoising which regularize or convexify the problem. Finally, an application on real Diffusion Tensor Images, a strongly affected by rician noise MRI modality, is presented and discussed.

Low Complexity Iterative Receiver Design for Shallow Water Acoustic Channels

An adaptive iterative receiver structure for the shallow underwater acoustic channel (UAC) is proposed using a decision feedback equalizer (DFE) and employing bit-interleaved coded modulation with iterative decoding (BICM-ID) in conjunction with adaptive Doppler compensation. Experimental results obtained from a sea trial demonstrate that the proposed receiver not only reduces inherent problem of error propagation in the DFE but also improves its convergence, carrier phase tracking, and Doppler estimation. Furthermore, simulation results are carried out on UAC, modelled by utilizing geometrical modelling of the water column that exhibits Rician statistics and a long multipath spread resulting in severe frequency selective fading and intersymbol interference (ISI). It has been demonstrated that there is a practical limit on the number of feedback taps that can be employed in the DFE and data recovery is possible even in cases where the channel impulse response (CIR) is longer than the span of the DFE. The performance of the proposed receiver is approximately within 1 dB of a similar system employing DFE and turbo code, however, at a significantly reduced computational complexity and memory requirements, making our system attractive for real-time implementation.

Experimental checking of the Rician statistics in partially compensated wavefronts

Atmospheric turbulence imposes a limit on the resolution attainable by large ground-based telescopes. In the visible, adaptive optics (AO) systems can only partially compensate turbulence-induced distortions. Hence, the light intensity at the telescope image plane is a random variable. In order to check the light intensity statistics we have developed an experimental setup that simulates simultaneously the atmosphere and the AO effects. Phase modulation is produced by LCDs extracted from a commercial projector. It is shown that experimental histograms of the light intensity at the image plane fit the theoretical Rician distribution.

Efficient Gabor filter design for texture segmentation

Gabor filters have been successfully applied to a broad range of image processing tasks. The present paper considers the design of a single filter to segment a two-texture image. A new efficient algorithm for Gabor-filter design is presented, along with methods for estimating filter output statistics. The algorithm draws upon previous results that showed that the output of a Gabor-filtered texture is modeled well by a Rician distribution. A measure of the total output power is used to select the center frequency of the filter and is used to estimate the Rician statistics of the Gabor-filtered image. The method is further generalized to include the statistics of postfiltered outputs that are generated by a Gaussian filtering operation following the Gabor filter. The new method typically requires an order of magnitude less computation to design a filter than a previously proposed method. Experimental results demonstrate the efficacy of the method.

Gabor filter design for multiple texture segmentation

A method is presented for the design of a single Gabor filter for the segmentation of multitextured images. Earlier methods were limited to filters designed for one or two textures or to filters selected from a predetermined filter bank. Our proposed method yields new insight into the design of Gabor filters for segmenting multitextured images and lays an essential foundation for the design of multiple Gabor filters. In the method, Rician statistics of filtered textures at two different Gabor-filter envelope scales are used to efficiently generate probability density estimates for each filtered texture over an extensive set of candidate filter parameters. Variable degrees of postfiltering and the accompanying effect on postfilter output statistics are also included in the design procedure. The result is a unified framework that analytically relates the texture power spectra, Gabor-filter parameters, postfiltering effects, and image-segmentation error. Finally, the resulting filter design is based on all constituent textures and is not constrained to a limited set of candidate filters.

Downlink DS CDMA performance over a mobile satellite channel

Code division multiple access (CDMA) has been proposed for personal communications networks for both terrestrial and satellite links. We analyze the performance of the downlink (i.e., the base-to-mobile link) of a low earth orbiting (LEO) mobile satellite channel. An important characteristic of this fading channel is that the desired signal and the multiple access interference from all spot beams of the corresponding satellite fade simultaneously. In this respect, the satellite downlink is also different from its terrestrial counterpart. A two-state fading channel model is considered. In the nonshadowed state, the signal envelope is characterized by Rician statistics and in the shadowed state by the Rayleigh statistics. We analyze the probability of error performance when coherent detection, diversity, spectrum sharing by two service providers, and forward error correction are employed.

Group-delay tracking in optical stellar interferometry with the fast Fourier transform

Group-delay tracking is a method of fringe tracking used for optical stellar interferometry. It employs a photon-counting spectrometer to record short-exposure frames of channeled spectra. In each frame the number of fringes is proportional to the path difference, which can be extracted by power spectrum analysis. In this study the low-light-level limitations of the method are examined when the fast Fourier transform is used for data processing. Frame times are limited by the coherence time of the atmosphere, and for active tracking the sensitivity depends on the largest number of power spectra that can be integrated usefully. Rayleigh and Rician statistics are used to model the visibility amplitudes determined from the power spectra, and the probability of tracking loss is examined as a function of fringe visibility, the number of photons per frame, and the number of integrated frames. The effect of bracketing the fringe peak with a filter is also examined, and simulations are used to verify the predictions.

DPSK performance for indoor wireless Rician fading channels

Indoor wireless channels which fade because of reflections from the building structure and the objects within the building have been experimentally found to fit either Rayleigh or Rician statistics. Digital communications performance has been calculated for these models, although in the Rician case numerical methods are typically employed. The authors present the closed form solution for DPSK in slow, flat, Rician fading, specifically for those values of specular-to-random ratio which have been determined experimentally to characterize Rician fading indoor environments. They then determine the performance loss as a function of the specular-to-random ratio. Finally, the results are generalized for a packet of N bits. Several useful approximations are also presented. >

Performance analysis of microcellular mobile radio systems with shadowed cochannel interferers

A study is presented of microcellular mobile radio systems where the desired signal has Rician statistics and cochannel interferers experience lognormal shadowing as well as Rayleigh fading. This implies a Rician/Rayleigh-plus-lognormal microcell interference model. The probability density function of the signal-to-interference ratio is derived and used to evaluate the performance of microcellular systems in terms of the outage probability.

Bit error probabilities of NCFSK and DPSK signals in microcellular mobile radio systems

Microcellular mobile radio systems are studied where the desired signal has Rician statistics and the cochannel interferers experience Rayleigh fading. The probability density function of the signal-to-interference ratio is derived and is used to obtain the bit error probabilities of noncoherent frequency shift-keying and differential phase shift-keying signals.

Identification of periodic, specular, and diffusely scattering structures in skeletal muscle and tissue-mimicking phantoms via generalized Rician statistics

Identification of periodic, specular, and diffusely scattering structures in skeletal muscle and tissue-mimicking phantoms via generalized Rician statistics

Rician statistics and signal detectability in ultrasonic B-scans

Rician statistics and signal detectability in ultrasonic B-scans

On the statistics of scintillating signals

The statistics that best describe optical and radio signals that have been scattered by random refractive-index irregularities have presented an open question for some time. Different models have been used close to the medium (log-normal) and far from it (Rician), and signal behavior in the intermediate zone has been particularly difficult to characterize. In this work, we address experimentally the problem of a general and systematic description in all Fresnel-zone regimes and for all strengths of scatter. We make use of multifrequency, phase-coherent radio signals transmitted through the ionosphere to obtain a bivariate representation of complex-signal statistics and then form conclusions based on chi-square tests of four hypotheses against histograms of intensity and phase. We find that neither the log-normal nor the Gaussian generalization of Rician statistics provides a generally valid and complete description of scintillation but that a two-component model based upon them does. We suggest, further, that equal or superior efficacy might be achieved from a simpler model based on the Nakagami distribution for intensity and the normal distribution for phase. At present no such model exists that can also account for correlation between intensity and phase, which is a salient feature of our observations.

Probability density function of the intensity of light reflected from a moderately rough surface in the far field

A general expression for the probability density function P(I) of the intensity of light reflected from a moderately rough surface in the far field is derived by the cumulant expansion of the random variable. It is shown that P(I) satisfies the modified Rician statistics for some general surface models in the limit of large L/T, where L is the dimension of the illuminating area, and T is the correlation length.

A Conditional-Test Sign Detector for Nonparametric Radar

The performance of a four-level sign detector in constant false-alarm rate (CFAR) radar is investigated. The detector uses a single independent reference noise observation per sweep and the nonparametric property is obtained through the use of a conditional statistical test. Detection performance is evaluated for the specific case of white Gaussian background noise with Rician statistics for signal plus noise. Both the asymptotic and finite-sample detection performance is determined and found to be significantly better compared with the sign detector.

The Relation Between the Specular-to-Interference Ratio and the Scintillation Index

This concise paper points out evidence that in many cases the fluctuations in a signal transmitted through ionospheric irregularities do not obey Rician statistics and that therefore, the Rician relation between the specular-to-interference ratio and the scintillation index, recently discussed by Shaft, may not apply to ionospheric communications studies in these cases.