The recovery of the initial pressure rise distribution tends to be an ill-posed problem in the presence of noise and when limited independent data is available, necessitating regularization. The standard regularization schemes include Tikhonov, l1 -norm, and total-variation. These regularization schemes weigh the singular values equally irrespective of the noise level present in the data. This work introduces a fractional framework to weigh the singular values with respect to a fractional power. This fractional framework was implemented for Tikhonov, l1-norm, and total-variation regularization schemes. The fractional framework outperformed the standard regularization schemes by 54% in terms of observed contrast/signal-to-noise-ratio.
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