TY  - JOUR
AB  - Remote sensing observations from satellites and global biogeochemical models have combined to revolutionize the study of ocean biogeochemical cycling, but comparing the two data streams to each other and across time remains challenging due to the strong spatial-temporal structuring of the ocean. Here, we show that the Wasserstein distance provides a powerful metric for harnessing these structured datasets for better marine ecosystem and climate predictions. The Wasserstein distance complements commonly used point-wise difference methods such as the root-mean-squared error, by quantifying differences in terms of spatial displacement in addition to magnitude. As a test case, we consider chlorophyll (a key indicator of phytoplankton biomass) in the northeast Pacific Ocean, obtained from model simulations, in situ measurements, and satellite observations. We focus on two main applications: (i) comparing model predictions with satellite observations, and (ii) temporal evolution of chlorophyll both seasonally and over longer time frames. The Wasserstein distance successfully isolates temporal and depth variability and quantifies shifts in biogeochemical province boundaries. It also exposes relevant temporal trends in satellite chlorophyll consistent with climate change predictions. Our study shows that optimal transport vectors underlying the Wasserstein distance provide a novel visualization tool for testing models and better understanding temporal dynamics in the ocean.
AU  - Hyun, S.*
AU  - Mishra, A.*
AU  - Follett, C.L.*
AU  - Jönsson, B.*
AU  - Kulk, G.*
AU  - Forget, G.*
AU  - Racault, M.F.*
AU  - Jackson, T.*
AU  - Dutkiewicz, S.*
AU  - Müller, C.L.
AU  - Bien, J.*
C1  - 65517
C2  - 52710
TI  - Ocean mover's distance: Using optimal transport for analysing oceanographic data.
JO  - Proc. R. Soc. London A
VL  - 478
IS  - 2262
PY  - 2022
SN  - 1364-5021
ER  - 

TY  - JOUR
AB  - Optoacoustic imaging was for a long time concerned with the reconstruction of energy density or optical properties. In this work, we present the full inverse problem with respect to optical absorption and diffusion as well as speed of sound and mass density. The inverse problem is solved by an iterative gradient-based optimization procedure. Since the ill-conditioning increases with the number of sought parameters, we propose two approaches to improve the conditioning. The first approach is based on the reduction of the size of the basis for the parameter spaces, that evolves according to the particular characteristics of the solution, while maintaining the flexibility of element-wise parameter selection. The second approach is a material identification technique that incorporates prior knowledge of expected material types and uses the acoustical gradients to identify materials uniquely. We present numerical studies to illustrate the properties and functional principle of the proposed methods. Significant convergence speed-ups are gained by the two approaches countering ill-conditioning. Additionally, we show results for the reconstruction of a mouse brain from in vivo measurements.
AU  - Schoeder, S.*
AU  - Olefir, I.
AU  - Kronbichler, M.*
AU  - Ntziachristos, V.
AU  - Wall, W.A.*
C1  - 54955
C2  - 45987
CY  - 6-9 Carlton House Terrace, London Sw1y 5ag, England
TI  - Optoacoustic image reconstruction: The full inverse problem with variable bases.
JO  - Proc. R. Soc. London A
VL  - 474
IS  - 2219
PB  - Royal Soc
PY  - 2018
SN  - 1364-5021
ER  - 

TY  - JOUR
AB  - Signals with discontinuities appear in many problems in the applied sciences ranging from mechanics, electrical engineering to biology and medicine. The concrete data acquired are typically discrete, indirect and noisy measurements of some quantities describing the signal under consideration. The task is to restore the signal and, in particular, the discontinuities. In this respect, classical methods perform rather poor, whereas non-convex non-smooth variational methods seem to be the correct choice. Examples are methods based on Mumford-Shah and piecewise constant Mumford-Shah functionals and discretized versions which are known as Blake- Zisserman and Potts functionals. Owing to their non-convexity, minimization of such functionals is challenging. In this paper, we propose a new iterative minimization strategy for Blake-Zisserman as well as Potts functionals and a related jump-sparsity problem dealing with indirect, noisy measurements. We provide a convergence analysis and underpin our findings with numerical experiments.
AU  - Weinmann, A.
AU  - Storath, M.*
C1  - 44387
C2  - 36933
CY  - London
TI  - Iterative Potts and Blake-Zisserman minimization for the recovery of functions with discontinuities from indirect measurements.
JO  - Proc. R. Soc. London A
VL  - 471
IS  - 2176
PB  - Royal Soc
PY  - 2015
SN  - 1364-5021
ER  -