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A Review on Data Fusion of Multidimensional Medical and Biomedical Data
Data fusion aims to provide a more accurate description of a sample than any one source of data alone. At the same time, data fusion minimizes the uncertainty of the results by combining data from multiple sources. Both aim to improve the characterization of samples and might improve clinical diagnosis and prognosis. In this paper, we present an overview of the advances achieved over the last decades in data fusion approaches in the context of the medical and biomedical fields. We collected approaches for interpreting multiple sources of data in different combinations: image to image, image to biomarker, spectra to image, spectra to spectra, spectra to biomarker, and others. We found that the most prevalent combination is the image-to-image fusion and that most data fusion approaches were applied together with deep learning or machine learning methods.
A function space framework for structural total variation regularization with applications in inverse problems
In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable TV type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted TV for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.