The following paper asks an interesting question and puts sparsity/positivity promoting algorithms in a positive light. Instead of using Least Squares for overcomplete systems, one can use a different inversion based on LASSO that provides something useful. The field of atmospheric science being so empirical, one always wonder if something interesting can be gotten out of forward simulation models. And indeed as they say in the paper, the difference between sensor readings and computer models could provide some sorts of correlation but, sometines, " the variability is considerable—often orders of magnitude." It turns out that if the current result of the paper holds, there is an interesting question at the end of this paper that should have a bearing on the current imaging of the deteriorated cores (see Imaging Damaged Reactors and Volcanoes ). But first, here is the paper, go read it, I'll read it :The Fukushima Inverse Problem by Marta Martinez-Camara, Ivan Dokmanic, Juri Ranieri, Robin Scheibler and Martin Vetterli, Andreas Stohl
Knowing what amount of radioactive material was released from Fukushima in March 2011 is crucial to understand the scope of the consequences. Moreover, it could be used in forward simulations to obtain accurate maps of deposition. But these data are often not publicly available, or are of questionable quality. We propose to estimate the emission waveforms by solving an inverse problem. Previous approaches rely on a detailed expert guess of how the releases appeared, and they produce a solution strongly biased by this guess. If we plant a nonexistent peak in the guess, the solution also exhibits a nonexistent peak. We propose a method based on sparse regularization that solves the Fukushima inverse problem blindly. Together with the atmospheric dispersion models and worldwide radioactivity measurements our method correctly reconstructs the times of major events during the accident, and gives plausible estimates of the released quantities of Xenon.
The attendant code is here, it features the transport matrix A and the cleaning code. The code uses CVX.
I find it fascinating that one needs to enforce the positivity of the solutions. I wonder if by using the Xe and the Cs data there would not be a way to figure out where out of the three or four potential sources, the ones that emitted shortly after the earthquake.
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