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A possible result is a blurred estimate of the true effect which might underestimate differences between treatment groups.
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The system spatial resolution was calculated as where s is the manufacturer-characterized spot size measured per the British Standard Method [ 17] and d ≈ 33 μm is the spatial detector blur estimated from a measured edge-spread function.
Additionally, the proposed multi-scale approach allows user to automatically initialize the proposed algorithm without visually inspecting the observed blurred image for determining the initial blur estimate.
At the lowest resolution the initial blur estimate (i.e., h1) is set to the uniform blur and the lowest resolution of the down-sampled observed image is utilized as the initial image estimate (i.e., x1).
The multi-scale approach consists of down-sampling the blurred photograph to number of low resolution images, and by utilizing the proposed algorithm iteratively to obtain the blur estimate at each resolution.
By analyzing the observed blurred image it is possible to come up with more informative initial blur estimates; however in this study our focus is to develop a completely automated algorithm once the blur support is provided.
This iterative process is repeated until the algorithm converges and image and blur estimates are obtained at their native resolutions.
To avoid unrealistic blur estimates we adopt here a multi-scale scheme similar in spirit to the one proposed in [12].
After convergence is achieved at each scale we up-sample the image and the blur estimates to the next higher resolution and re-run the proposed algorithm.
Alternatively, the authors in [13, 14] introduced heuristic re-weighting of the regularization parameters, at each iteration, to prevent the algorithms from converging to unrealistic blur estimates.
After each iteration, we enforce the following constraints on the blur estimates: the positivity (blur elements less than zero are set to zero), the support constraint (blur elements outside of the blur support estimate are set to zero), and the energy conservation (sum of the blur elements equals one).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com