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My first research interests were in non-relativistic quantum scattering theory. In particular I worked on Regge pole theory and on its applications to nuclear physics, on spectral properties of Schroedinger operators with nonlocal potentials and on some mathematical problems arising in the optical model of nuclear reactions. Around 1975 my interest was addressed to another research domain which was new at that time: the theory and the applications of inverse and ill-posed problems. After some preliminary work on deterministic and probabilistic regularization methods and on their applications to the problem of object restoration in optics, I developed methods based on the singular value decomposition of a linear operator for the solution of inverse problems in various domains of applied science. In particular, properties of the singular system of the finite Laplace transform were derived and used for data inversion in the problem of polydispersity analysis by means of photon correlation spectroscopy. Moreover, applications of the theory to imaging problems in microscopy suggested a new version of the confocal scanning microscope. A prototype of this new microscope was realized by E.R.Pike at King's College in London. Other applications were to particle sizing in the micron and submicron region by light scattering, to microwave thermography, seismic tomography and astrophysics. Subsequent research interests were in problems of image restoration in infrared astronomy, in microscopy and in medical imaging, including SPECT imaging and chirp-pulse microwave computed tomography. Presently I am working on the application of efficient optimization methods to large scale inverse problems with data affected by the so-called Poisson noise, namely the noise due to fluctuations in photon counting.
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ANNALI DELL'UNIVERSITA' DI FERRARAno. 2 (2022): 259-275
Introduction to Inverse Problems in Imagingpp.183-212, (2021)
Introduction to Inverse Problems in Imagingpp.105-132, (2021)
Computational Methods for Inverse Problems in ImagingSpringer INdAM Seriespp.117-140, (2019)
INVERSE IMAGING WITH POISSON DATA: FROM CELLS TO GALAXIESpp.1-340, (2018)
INVERSE IMAGING WITH POISSON DATA: FROM CELLS TO GALAXIES (2018)
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