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Modeling the amplitude statistics of ultrasonic images
 IEEE Trans Med Imaging
"... Abstract—In this paper, a new statistical model for representing the amplitude statistics of ultrasonic images is presented. The model is called the Rician inverse Gaussian (RiIG) distribution, due to the fact that it is constructed as a mixture of the Rice distribution and the Inverse Gaussian dis ..."
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Abstract—In this paper, a new statistical model for representing the amplitude statistics of ultrasonic images is presented. The model is called the Rician inverse Gaussian (RiIG) distribution, due to the fact that it is constructed as a mixture of the Rice distribution and the Inverse Gaussian distribution. The probability density function (pdf) of the RiIG model is given in closed form as a function of three parameters. Some theoretical background on this new model is discussed, and an iterative algorithm for estimating its parameters from data is given. Then, the appropriateness of the RiIG distribution as a model for the amplitude statistics of medical ultrasound images is experimentally studied. It is shown that the new distribution can fit to the various shapes of local histograms of linearly scaled ultrasound data better than existing models. A loglikelihood crossvalidation comparison of the predictive performance of the RiIG, the K, and the generalized Nakagami models turns out in favor of the new model. Furthermore, a maximum a posteriori (MAP) filter is developed based on the RiIG distribution. Experimental studies show that the RiIG MAP filter has excellent filtering performance in the sense that it smooths homogeneous regions, and at the same time preserves details. Index Terms—Compound distribution, generalized Nakagami distribution, K distribution, maximum a posteriori speckle filter, nonGaussian statistics, nonRayleigh amplitude statistics, speckle filtering, ultrasound amplitude statistics, ultrasound imaging. I.
Evolution of the Statistical Properties of Photons Passed through a TravelingWave Laser Amplifier
 IEEE J. Quantum Electron
, 1992
"... We determine the evolution of the photon statistics of a light beam as it passes through a travelingwave laser amplifier, modeled as a birthdeathimmigration (BDI) medium. The relationship between the input and output probability distributions and probability generating functions with given (but p ..."
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We determine the evolution of the photon statistics of a light beam as it passes through a travelingwave laser amplifier, modeled as a birthdeathimmigration (BDI) medium. The relationship between the input and output probability distributions and probability generating functions with given (but possibly varying) birth, death, and immigration rates for arbitrary input statistics is obtained. The case of constant birth, death, and immigration rates is considered in particular detail. The photon statistics at the output of a general BDI travelingwave amplifier are always broader than those at the input, and they can take many forms. Our most general solution can be applied when the input distribution to the amplifier takes the form of a negativebinomial transform. The results are expected to be useful in calculating the performance characteristics of lightwave systems using optical amplifiers in which the object is to detect light with a broad range of statistical properties, including scattered light, spontaneousemission light, and light emitted from a laser. In the latter case the input is Poisson, and the output distribution assumes the form of a noncentralnegativebinomial (Laguerre) distribution which is usually associated with a multimode (phasepreserving) superposition of coherent and chaotic fields.
Cascaded Stochastic Processes in Optics
 Traitement du Signal
, 1999
"... Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem: how an optical field is converted into a sequence of photoelectrons upon detection. Their choice of problem could not have been better, nor their timing more judicious. In a paper entitled "Photoe ..."
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Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem: how an optical field is converted into a sequence of photoelectrons upon detection. Their choice of problem could not have been better, nor their timing more judicious. In a paper entitled "Photoelectron Shot Noise", published in the Journal of Mathematical Physics in 1970, when quantum optics was in its infancy, they obtained results that were to serve as an important building block in analyzing and generating many di#erent forms of light. We present some variations on the theme of cascaded stochastic processes in optics. Processus stochastiques en cascade d'importance en optique ResumeIl y a trente ans, Bernard Picinbono et ses collegues ont traite rigoureusement un probleme important : comment un champ optique est converti en une suite de photoelectrons apres detection. Leur choix de ce probleme ne pouvait pas etre meilleur et a revele un caractere pionnier. Dans un article intitule "Photoelectron Shot Noise", publie dans le Journal of Mathematical Physics en 1970, alors que l'optique quantique n'etait encore qu'a ses debuts, ils obtinrent des resultats qui constituerent un important point de depart pour analyser et generer de nombreuses et diverses formes de lumieres. Nous presentons des variations sur le theme des processus stochastiques en cascade, en optique. 1
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"... Cascaded stochastic processes in optics Processus stochastiques en cascade d'importance en optique abstract and key words Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem: how an optical field is converted into a sequence of photoelectrons upon det ..."
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Cascaded stochastic processes in optics Processus stochastiques en cascade d'importance en optique abstract and key words Thirty years ago, Bernard Picinbono and his colleagues carefully addressed an important problem: how an optical field is converted into a sequence of photoelectrons upon detection. Their choice of problem could not have been better, nor thei r timing more judicious. In a paper entitled &quot;Photoelectron Shot Noise&quot;, published in the Journal of Mathematical Physics in 1970, when quantum optics was in its infancy, they obtained results that were to serve as an important building block i n analyzing and generating many different forms of Tight. We present some variations on the theme of cascaded stochasti c processes in optics. Poisson process, shot noise, selfexciting process, doublystochastic process, compound Poisson process, doublyPoisson, triggered optical emissions, multiplyPoisson, cascadedPoisson, correlatedPoisson, nonclassical light, subPoisson light. résumé et mots clés Il y a trente ans, Bernard Picinbono et ses collègues ont traité rigoureusement un problème important: comment un champ optiqu e est converti en une suite de photoélectrons après détection. Leur choix de ce problème ne pouvait pas être meilleur et a révélé u n