system from its output knowing its Impulse Response Function (IRF). When the IRF of the system is ... the generating model of the observations. Finally, I present ...
Title: Bayesian Blind Deconvolution Abstract: Deconvolution consists in estimating the input of a linear and invariant system from its output knowing its Impulse Response Function (IRF). When the IRF of the system is unknown, we are face to Blind Deconvolution. This inverse problem is ill-posed and needs prior information to obtain a satisfactory solution. Regularization theory, well known for simple deconvolution, is no more enough to obtain a satisfactory solution. Bayesian inference approach with appropriate priors on the unknown input as well as on the IRF has been used successfully, in particular with a Gaussian prior on the IRF and a sparsity enforcing prior on the input. Joint Maximum A posteriori (JMAP), Expectation-Maximization (EM) algorithm for marginalized MAP and Variational Bayesian Approximation (VBA) are the methods which have been considered recently with some advantages for the last one. In this talk, first I review these methods and give some original insights by comparing them, in particular for their respective properties, advantages and drawbacks and their computational complexity. Then, I propose to use a Student-t prior law for the unknown input which has the property of sparsity enforcing and which gives the possibility to give a hierarchical graphical structure for the generating model of the observations. Finally, I present detailed algorithms of JMAP, EM and VBA for the joint estimation of the input, the IRF and the hidden variables of the infinite Gaussian mixture model of the Student-t probability law. At the end, I will show some applications in geophysical signal processing as well as in hyperspectral image processing.
Dec 9, 2014 - Forward model: 2D Convolution ... obtained from the elements of the impulse response h(t) or the Point Spread ... Forward model g = H f + Ç«.
re-invented, first by Gull and Skilling [42] who called the clean beam the Intrinsic .... neously recorded in the wave-front sensor (WFS); these data contain ...
(15) where c is a constant which will be eliminated since after, and that. < â ln p(f ..... IEEE. Trans Neural Netw, vol. 15, no. 2, pp. 455â459, Mar 2004. [Online].
Csi(Ï1,Ï2,Ï3) =0 (< â), (22). Ki = Kj, i, j = 1, à¸à¸à¸,n; i = j. (23). Here Z denotes the set of all integers and Cν(Ï1,Ï2,Ï3) is the fourth-order auto-cumulant function of ...
Blind deconvolution (BD): Signal model, basic assumptions .... An estimator of the source sequence having form B(zm,n) ..... ISI (dB) Flops Time (sec.s).
multi-layer perceptron (MLP) structures endowed with filtering synapses (a review of .... denotes the convolution between the system's impulse response and the ...
Oct 23, 2018 - âblurred signalâ for example) and one tries recovering the preimage of ... 1 The density could be k1B(0,r) where r > 0 is a radius and k = (Ïr2)â1. ..... As measures spaces, RZ â¼ M(Z) (the space of all measures on Z) and.
depends mainly on the dimensions of the waveguide, the operating frequency, the ... Unlike the plane-wave far-field approach, the PSF associated with these.
images by use of object and point-spread function power spectra,â Appl. Opt. 37, ... In Section 4, we derive a marginal estimator and show its performance on ...
deconv Cf. Estimated PSF Ch. Estimated Cf. A. Mohammad-Djafari, Bayesian Blind Deconvolution of sparse images with a Student-t a priori model, IPAS 2014: ...
Abstract: We propose a set of statistical constraints for the problem of imaging through atmospheric turbulence. The constraints, in the form of probability density ...
Sep 16, 2018 - 1 The density could be k1B(0,r) where r > 0 is a radius and k = (πr2)−1. Question in dimension 2: is it a zero divisor for convolution? We will see ...
A common value of 1.2'' for seeing and 1 µm wavelength was adopted. ... be described by a stationary Gaussian prior probability distribution with mean value ( ), .... Imaging Through Turbulence Using Principal Component Analysis".
Since actual probability density function (PDF) of the object is in general not known ... To model short-exposure PSF statistics use is made of the gamma PDF [4]:.
the sense of the maximum a posteriori is based on a simulated annealing ... to control the law for the image and one parameter to control the law for the noise.
particularly appropriate for the modeling of luminosity expo- nential and laws. 1/4 r. The priors reviewed above can be extended to more complex models.
Nov 26, 2008 - metric application between G and Gk. If Hk is the linear ope- rator associated to ... But, on the light of the experimental results, we consider this.
Various numerical evaluations provide encouraging results despite the strong ... Bayes; Potts; unsupervised learning; sampling; optimization .... segmentation from indirect data (inversion-segmentation) also based a Potts model for the labels.
images must be deconvolved to restore the fine details of the object. ... restoration with a good photometric precision because of the inevitable noise in the im-.
host-cell adhesion, inflammation and immune activation. In this contribution, we compare the flexibility and the organization of PG from Gram- negative bacteria ...
Transient protein interactions by NMR and SAXS. M. Pons a,b. , P. Bernadó a. , J. Blobel a a Institute for Research in Biomedicine (IRB-Barcelona), Baldiri ...
developed robust methods to quantitatively describe these molecular ... analytical and numerical approaches to develop a self-consistent representation of all ...