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The idea for this text emerged over several years as the authors participated in research projects related to analysis of data from NASA's RHESSI Small Explorer mission. The data produced over the operational lifetime of this mission inspired many investigations related to a specific science question: the when, where, and how of electron acceleration during solar flares in the stressed magnetic environment of the active Sun.
A vital key to unlocking this science problem is the ability to produce high-quality images of hard X-rays produced by bremsstrahlung radiation from electrons accelerated during a solar flare. The only practical way to do this within the technological and budgetary limitations of the RHESSI era was to opt for indirect modalities in which imaging information is encoded as a set of two-dimensional spatial Fourier components. 
Radio astronomers had employed Fourier imaging for many years. However, differently than for radio astronomy, X-ray images produced by RHESSI had to be constructed from a very limited number of sparsely distributed and very noisy Fourier components. Further, Fourier imaging is hardly intuitive, and extensive validation of the methods was necessary to ensure that they produced images with sufficient accuracy and fidelity for scientific applications.
This book summarizes the results of this development of imaging techniques specifically designed for this form of data. It covers a set of published works that span over two decades, during which various imaging methods were introduced, validated, and applied to observations. Also considering that a new Fourier-based telescope, STIX, is now entering its nominal phase on-board the ESA Solar Orbiter, it became more and more apparent to the authors that it would be a good idea to put together a compendium of these imaging methods and their applications. Hence the book you are now reading. 

Hard X-Ray Imaging of Solar Flares

1 Hard X-ray Emission in Solar Flares1.1 A Brief Overview of Solar Flares1.2 Hard X-Ray Emission from Flares and its Significance1.2.1 Acceleration of Nonthermal Electrons1.2.2 Hard X-Ray Production by Accelerated Electrons: The Bremsstrahlung Process1.2.3 Relation of the Mean Source Electron Spectrum to the Accelerated Spectrum1.3 History of Solar Hard X-Ray Imaging Observations2 X-Ray Imaging Methods2.1 Medical Imaging2.2 Astrophysical X-ray Imaging Techniques2.2.1 Absorption2.2.2 Scattering2.2.3 Reflection2.2.4 Diffraction3 RHESSI and STIX3.1 RHESSI Design / Brief History of Concept Development3.2 The RHESSI imaging concept3.3 Strengths and Limitations of the RHESSI RMC Imaging Technique3.4 RHESSI Imaging Example3.5 SSW and the RHESSI GUIs3.6 STIX Design / Brief History of Concept Development3.7 The STIX imaging concept3.8 STIX software3.9 RHESSI vs. STIX - a comparison of strengths and limitations4 Image Reconstruction Methods4.1 The Essence of the Image Reconstruction Problem4.1.1 Count-based versus visibility-based imaging4.1.2 Point Spread Functions4.2 The ill-posedness of the image reconstruction problem4.3 The Regularization Concept4.4 Numerical Optimization5 Count-based Imaging Methods5.1 Back-projection5.2 CLEAN5.2.1 Two-step CLEAN Method5.3 Forward Fit5.4 Pixon5.4.1 Maximum Entropy Methods5.4.2 The Pixon Methodology5.5 Expectation Maximization6 Visibility-based Imaging Methods6.1 Visibilities6.2 Visibility-based Methods6.3 VIS_FWDFIT6.4 Bayesian Optimization6.5 MEM_NJIT and MEM_GE6.6 uv_smooth6.7 VIS_CLEAN and Multi-scale CLEAN6.8 Compressed Sensing - VIS_CS and VIS_WV6.9 Electron Flux Maps7 Application to Solar Flares7.1 Number and Nature of Hard X-Ray Sources in the 2002 February 20 Event7.2 The Physical Nature of Multiple Hard X-Ray Sources in the 2002 July 23 Event7.3 Properties of the Electron Acceleration Region7.3.1 Using the VIS_FWDFIT method to estimate the acceleration region length and density7.3.2 Using the MEM_NJIT method to revisit earlier results7.4 Empirical Determination of the Electron Energy Loss Rate7.5 Hard X-Ray Imaging and the Global Energetics of Solar Flares8 Future Possibilities8.1 STIX8.2 NuSTAR8.3 FOXSI8.4 Advanced Spaced-based Solar Observatory8.5 GRIPS8.6 Hard X-ray Polarimetry8.7 ConclusionReferencesIndex