Image Estimation and Uncertainty Quantification
Image Estimation and Uncertainty Quantification
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Date
2015
Authors
Taroudaki, Viktoria
Advisor
O'Leary, Dianne P
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Abstract
Recorded images are usually contaminated by blur and noise. The restoration
of such altered images is an ill-posed problem. Even if the blur is known, the
unknown noise leads to uncertainty in the restored image. The naive restoration
approach fails since it contains a lot of noise at high frequencies that destroys the
computed restored image. To remedy this problem, this work focuses on the computation
of the restored image by using spectral filters that give weight to components
of the image that are not so contaminated by noise. We use different filtering methods
such as the Truncated Tikhonov, Truncated SVD, and new methods that we
created here and we seek to find a near optimal choice of the filter parameter which
will give the best approximation of the original image. We define and compute the
Picard Parameter when the problem satisfies the Discrete Picard Condition, and
with that we estimate the noise properties. Also, we develop a new method to compute
the near optimal solution by using statistical analysis which also gives us a way
to estimate the error of the solution, a way to quantify uncertainty.