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    A function space framework for structural total variation regularization with applications in inverse problems
    (Bristol [u.a.] : Inst., 2018) Hintermüller, Michael; Holler, Martin; Papafitsoros, Kostas
    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.
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    Lab::Measurement—A portable and extensible framework for controlling lab equipment and conducting measurements
    (Amsterdam : North Holland Publ. Co., 2019) Reinhardt, S.; Butschkow, C.; Geissler, S.; Dirnaichner, A.; Olbrich, F.; Lane, C.E.; Schröer, D.; Hüttel, A.K.
    Lab::Measurement is a framework for test and measurement automatization using Perl 5. While primarily developed with applications in mesoscopic physics in mind, it is widely adaptable. Internally, a layer model is implemented. Communication protocols such as IEEE 488 [1], USB Test & Measurement [2], or, e.g., VXI-11 [3] are addressed by the connection layer. The wide range of supported connection backends enables unique cross-platform portability. At the instrument layer, objects correspond to equipment connected to the measurement PC (e.g., voltage sources, magnet power supplies, multimeters, etc.). The high-level sweep layer automates the creation of measurement loops, with simultaneous plotting and data logging. An extensive unit testing framework is used to verify functionality even without connected equipment. Lab::Measurement is distributed as free and open source software. Program summary: Program Title: Lab::Measurement 3.660 Program Files doi: http://dx.doi.org/10.17632/d8rgrdc7tz.1 Program Homepage: https://www.labmeasurement.de Licensing provisions: GNU GPL v23 Programming language: Perl 5 Nature of problem: Flexible, lightweight, and operating system independent control of laboratory equipment connected by diverse means such as IEEE 488 [1], USB [2], or VXI-11 [3]. This includes running measurements with nested measurement loops where a data plot is continuously updated, as well as background processes for logging and control. Solution method: Object-oriented layer model based on Moose [4], abstracting the hardware access as well as the command sets of the addressed instruments. A high-level interface allows simple creation of measurement loops, live plotting via GnuPlot [5], and data logging into customizable folder structures. [1] F. M. Hess, D. Penkler, et al., LinuxGPIB. Support package for GPIB (IEEE 488) hardware, containing kernel driver modules and a C user-space library with language bindings. http://linux-gpib.sourceforge.net/ [2] USB Implementers Forum, Inc., Universal Serial Bus Test and Measurement Class Specification (USBTMC), revision 1.0 (2003). http://www.usb.org/developers/docs/devclass_docs/ [3] VXIbus Consortium, VMEbus Extensions for Instrumentation VXIbus TCP/IP Instrument Protocol Specification VXI-11 (1995). http://www.vxibus.org/files/VXI_Specs/VXI-11.zip [4] Moose—Apostmodern object system for Perl 5. http://moose.iinteractive.com [5] E. A. Merritt, et al., Gnuplot. An Interactive Plotting Program. http://www.gnuplot.info/ © 2018 The Author(s)