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An Efficient Bayesian Framework for Uncertainty Quantification in Nonlinear Imaging Inverse Problems
Anuj Abhishek, Sakshi Arya, Madhu Gupta
Bayesian methods provide a natural framework for estimating a parameter in non-linear inverse problems and quantifying uncertainty in the estimation. However, when the forward mode…
Statistical microlocal analysis in two-dimensional X-ray CT
Anuj Abhishek, Alexander Katsevich, James W. Webber
In many imaging applications it is important to assess how well the edges of the original object, , are resolved in an image, , reconstructed from the measured dat…
Adaptive estimation of a function from its Exponential Radon Transform in presence of noise
Anuj Abhishek, Sakshi Arya
In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of funct…
Minimax optimal estimator in the stochastic inverse problem for exponential Radon transform
Anuj Abhishek
In this article, we consider the problem of inverting the exponential Radon transform of a function in the presence of noise. We propose a kernel estimator to estimate the true fun…