In this paper, the inverse problem of reconstructing reflectivity function of a medium is examined within a blind deconvolution framework. The ultrasound pulse is estimated using higher-order statistics, and Wiener filter is used to obtain the ultrasonic reflectivity function through wavelet-based models. A new approach to the parameter estimation of the inverse filtering step is proposed in th...

Abstract Reconstrution of light intensity fluctuations from photon-counting data is a typical ill-posed inverse problem for non-Hermitian transforming operator. Such problems cannot be solved with the help of eigenfunction representation which diagonalizes the operator and simplifies the regularization of a quasi-solution. We describe an analytical method to solve this inverse problem using the...

There is a certain excitement in vision science concerning the idea of applying the tools of Bayesian decision theory to explain our perceptual capacities. Bayesian models – or ‘predictive coding models’ – are thought to be needed to explain how the inverse problem of perception is solved, and to rescue a certain constructivist and Kantian way of understanding the perceptual process (Clark 2012...

We offer a new example of conformal invariance (local scale invariance) far from equilibrium-the inverse cascade of surface quasigeostrophic (SQG) turbulence. We show that temperature isolines are statistically equivalent to curves that can be mapped into a one-dimensional Brownian walk (called Schramm-Loewner evolution or SLEkappa). The diffusivity is close to kappa=4, that is, isotemperature ...

Using a network analyzer, several experiments for the frequency-domain characterization of the indoor radio channel in the 0.91.1-GHz band are performed. In the experiments, the frequency response measurements are taken at spatially distributed locations throughout the test area by fixing the receiver in a central location and moving the transmitter to different locations. The experiments were ...

Solving inverse problems in a complex, geologically realistic, and discrete model space and from a sparse set of observations is a very challenging task. Extensive exploration by Markov chain Monte Carlo (McMC) methods often results in considerable computational efforts. Most optimization methods, on the other hand, are limited to linear (continuous) model spaces and the minimization of an obje...

There has been significant interest in sparse inverse covariance estimation in areas such as statistics, machine learning, and signal processing. In this problem, the sparse inverse of a covariance matrix of a multivariate normal distribution is estimated. A Penalised LogLikelihood (PLL) optimisation problem is solved to obtain the matrix estimator, where the penalty is responsible for inducing...

In this paper, we propose two algorithms to solve a large class of linear inverse problems when the observations are corrupted by various types of noises. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian, Poisson, multiplicative, etc.) independently of the degradation operator. On the other hand, the regularization is constructed t...

Perturbation models are families of distributions induced from perturbations. They combine randomization of the parameters with maximization to draw unbiased samples. Unlike Gibbs’ distributions, a perturbation model defined on the basis of low order statistics still gives rise to high order dependencies. In this paper, we analyze, extend and seek to estimate such dependencies from data. In par...

This paper completes the statistical modeling of the Hubble ow when a Tully-Fisher type relation is used for estimating the absolute magnitude M a p + b from a line width distance indicator p. Our investigation is performed with the aim of providing us with a full understanding of statistical biases due to selection eeects in observation, regardless of peculiar velocities of galaxies. We show t...