A functional approach to estimation of the parameters of generalized negative binomial and gamma distributions

The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and embraces Poisson distributions, negative binomial distributions, Sichel distributions, Weibull--Poisson distributions and many other types of distributions supplying descriptive statistics with many flexible models. These distributions seem to be very promising for the statistical description of many real phenomena. GG distributions are widely applied in signal and image processing and other practical problems. The statistical estimation of the parameters of GNB and GG distributions is quite complicated. To find estimates, the methods of moments or maximum likelihood can be used as well as two-stage grid EM-algorithms. The paper presents a methodology based on the search for the best distribution using the minimization of $\ell^p$-distances and $L^p$-metrics for GNB and GG distributions, respectively. This approach, first, allows to obtain parameter estimates without using grid methods and solving systems of nonlinear equations and, second, yields not point estimates as the methods of moments or maximum likelihood do, but the estimate for the density function. In other words, within this approach the set of decisions is not a Euclidean space, but a functional space.Comment: 13 pages, 6 figures, The XXI International Conference on Distributed Computer and Communication Networks: Control, Computation, Communications (DCCN 2018

SOLUS: An innovative multimodal imaging system to improve breast cancer diagnosis through diffuse optics and ultrasounds

To improve non-invasively the specificity in the diagnosis of breast cancer after a positive screening mammography or doubt/suspicious ultrasound examination, the SOLUS project developed a multimodal imaging system that combines: B-mode ultrasound (US) scans (to assess morphology), Color Doppler (to visualize vascularization), shear-wave elastography (to measure stiffness), and time domain multi-wavelength diffuse optical tomography (to estimate tissue composition in terms of oxy- and deoxy-hemoglobin, lipid, water, and collagen concentrations). The multimodal probe arranges 8 innovative photonic modules (optodes) around the US transducer, providing capability for optical tomographic reconstruction. For more accurate estimate of lesion composition, US-assessed morphological priors can be used to guide the optical reconstructions. Each optode comprises: i) 8 picosecond pulsed laser diodes with different wavelengths, covering a wide spectral range (635-1064 nm) for good probing of the different tissue constituents; ii) a large-area (variable, up to 8.6 mm2) fast-gated digital Silicon Photomultiplier; iii) the acquisition electronics to record the distribution of time-of-flight of the re-emitted photons. The optode is the basic element of the optical part of the system, but is also a stand-alone, ultra-compact (about 4 cm3) device for time domain multi-wavelength diffuse optics, with potential application in various fields

SOLUS: a novel multimodal approach to ultrasound and diffuse optics imaging of breast cancer

A multimodal instrument for breast imaging was developed, combining ultrasound (morphology), shear wave elastography (stiffness), and time domain multiwavelength diffuse optical tomography (blood, water, lipid, collagen) to improve the non-invasive diagnosis of breast cancer

Mimick Capacity Of Generalized Gamma Distribution For High Resolution SAR Image Statistical Modeling

International audienc

Mimic Capacity Of Fisher And Generalized Gamma Distributions For High Resolution SAR Image Statistical Modeling

International audienceThe aim of this paper is to compare the potentialof two popular flexible laws, the Fisher distribution and theGeneralized Gamma distribution, for the statistical modeling ofhigh-resolution SAR data through an original “mimicking-based”approach. The presented study allows to evaluate the ability ofboth laws to correctly imitate or “mimic” another reference law,frequently used for modeling the intensity of SAR images andchosen for instance as the K law or the Weibull, Beta or log-normal laws in this work. This study uses log-cumulant statisticsfor parameter estimation of the imitating law and involvesquantitative criteria of comparison based on the Kullback-Leiblerdivergences between the reference law and the Fisher law orthe Generalized Gamma law. The mimicking capacities of bothdistributions are first analyzed for some sets of parametersdescribing different studied cases, covering a wide set of possiblemimicked reference laws. The high modeling potential of bothdistributions is then illustrated on heterogeneous subscenes fromreal SAR intensity data. Pragmatical considerations are alsotaken into account to draw up recommendations about the pref-erential use of a distribution and to highlight complementaritiesof both Fisher and Generalized Gamma distributions, along withlimitations of the approach.</p

Capacites d’imitation de la loi Gamma Generalisee pour la modelisation statistique d’images radar haute resolution.

National audienc

Mimick Capacity Of Generalized Gamma Distribution For High Resolution SAR Image Statistical Modeling

International audienc

Mimic Capacity Of Fisher And Generalized Gamma Distributions For High Resolution SAR Image Statistical Modeling

International audienceThe aim of this paper is to compare the potentialof two popular flexible laws, the Fisher distribution and theGeneralized Gamma distribution, for the statistical modeling ofhigh-resolution SAR data through an original “mimicking-based”approach. The presented study allows to evaluate the ability ofboth laws to correctly imitate or “mimic” another reference law,frequently used for modeling the intensity of SAR images andchosen for instance as the K law or the Weibull, Beta or log-normal laws in this work. This study uses log-cumulant statisticsfor parameter estimation of the imitating law and involvesquantitative criteria of comparison based on the Kullback-Leiblerdivergences between the reference law and the Fisher law orthe Generalized Gamma law. The mimicking capacities of bothdistributions are first analyzed for some sets of parametersdescribing different studied cases, covering a wide set of possiblemimicked reference laws. The high modeling potential of bothdistributions is then illustrated on heterogeneous subscenes fromreal SAR intensity data. Pragmatical considerations are alsotaken into account to draw up recommendations about the pref-erential use of a distribution and to highlight complementaritiesof both Fisher and Generalized Gamma distributions, along withlimitations of the approach.</p