Shearlet-based regularization in statistical inverse learning with an application to x-ray tomography

Statistical inverse learning theory, a field that lies at the intersection of inverse problems and statistical learning, has lately gained more and more attention. In an effort to steer this interplay more towards the variational regularization framework, convergence rates have recently been proved for a class of convex, p-homogeneous regularizers with p (1, 2], in the symmetric Bregman distance. Following this path, we take a further step towards the study of sparsity-promoting regularization and extend the aforementioned convergence rates to work with .," p -norm regularization, with p (1, 2), for a special class of non-tight Banach frames, called shearlets, and possibly constrained to some convex set. The p = 1 case is approached as the limit case (1, 2) p → 1, by complementing numerical evidence with a (partial) theoretical analysis, based on arguments from "-convergence theory. We numerically validate our theoretical results in the context of x-ray tomography, under random sampling of the imaging angles, using both simulated and measured data. This application allows to effectively verify the theoretical decay, in addition to providing a motivation for the extension to shearlet-based regularization

VALUTAZIONE DELL'IMPIEGO DI TAMPONI SALIVARI SECCHI (DSS, DRIED SALIVA SWAB) PER LA DIAGNOSI E LO SCREENING NEONATALI DELL'INFEZIONE CONGENITA DA CYTOMEGALOVIRUS.

Background The identification of infected newborns at birth is necessary to prevent, or at least reduce, possible serious damages due to congenital Cytomegalovirus infection (cCMV). Viral isolation assay on saliva and urine specimens collected until the 14th day of birth is considered the gold standard method for cCMV\u2019s diagnosis, but it is a slow method and it needs specialized laboratories. Easy and inexpensive collection, handling and processing of samples are important for implementation of neonatal screening. The aim of this PhD project is to develop a method which could meet the requirements of a screening test: low cost (sampling, reagents and workload) with high sensibility and specificity; the second purpose is to identify a possible factor of poor prognosis. Material and Methods In this study dried saliva swabs or DSS, a nylon-flocked saliva swab (Copan) without any medium, were used to collect clinical specimens. The study was divided in four phases, each one divided in two steps: validation and clinical tests. In the 1st phase 410 DSS were collected from 21 babies with cCMV (follow-up group) and 365 from newborns or children who were in Mangiagalli\u2019s Hospital on July 2008 (random group). All DSS were extracted by commercial kit and the results were compared to classical saliva swabs or CSS collected and stored in Viral transport medium (VTM) at 4\ub0C. CSS were tested by rapid viral isolation (IR-p72) and nested-PCR in house (n-PCR). In the 2nd phase an extraction in-house was performed on DSS, and dried swabs were re-hydrated with E-MEM (cell\u2019s growth medium). 192 DSS were collected: 34 from a follow up group, 141 from children who attending preschool and 17 from babies with suspect of infection. All results were compared between DSS just agitated by vortex or extracted by thermal shock (ts) and CSS tested by nested-PCR. In the 3rd phase a commercial Real Time-PCR (RT-PCR) was performed for DSS vortexed or extracted by ts. Previously poor results were obtained with samples in E-MEM, therefore molecular grade water was preferred to re-hydrating DSS. 64 dried saliva swabs were collected from 45 follow-up children and 14 babies with suspect of infection. Results were compared between DSS tested in RT-PCR or n-PCR and CSS in n-PCR. In the 4th phase a genotyping methods were performed on DSS: RFLP (Restriction Fragment Length Polymorphism) for gB gene and, by collaboration with a Dutch group from LUMC (Leids Universitair Medisch Centrum), a Real Time-PCR in\u2013house for genes gB and gH. So 101 DSS were collected and tested from follow up group\u2019s children and suspected of infection. Results In every phase the sensibility between DSS and CSS was 100% regardless of treatment and studied groups. The specificity was 93% between DSS and CSS tested by IR-p72; it was higher if compered to CSS in n-PCR. In follow-up group the specificity was 58 and 70% between DSS and CSS in n-PCR. The most frequent genotype was gB1 both in RFLP (38%) and RT-PCR (34%). The most frequent gH strain was gH1 (48%). 19% of samples had mixed genotype of gB or gH or both; 3 patient (3%) had three gB strain in the same time. Conclusion Dried saliva swab is a good tool to detect CMV infection. Despite the treatments Low specificity in follow-up group is a consequence of high sensibility of DSS-test. In fact the babies of the follow up group had CMV infection, therefore the positive results might have been no false. Real Time-PCR (Argene) on DSS treated in molecular biology grade water gave optimal results. Pre-PCR treatments (vortexing or vortexing plus thermal shock), seem to have no influence. Genotyping from DSS by Real time-PCR could be a good alternative to genotyping from DBS (dried blood spots), because saliva has higher viral load. Confirmation of these data in a larger study will indicate that Real Time-PCR DSS testing (treat adding grade water and just vortexing), being simple and cheap , could be a suitable method for a neonatal cCMV infection screening

Deep Neural Networks for Inverse Problems with Pseudodifferential Operators: An Application to Limited-Angle Tomography

We propose a novel convolutional neural network (CNN), called \Psi DONet, designed for learning pseudodifferential operators (\Psi DOs) in the context of linear inverse problems. Our starting point is the iterative soft thresholding algorithm (ISTA), a well-known algorithm to solve sparsity-promoting minimization problems. We show that, under rather general assumptions on the forward operator, the unfolded iterations of ISTA can be interpreted as the successive layers of a CNN, which in turn provides fairly general network architectures that, for a specific choice of the parameters involved, allow us to reproduce ISTA, or a perturbation of ISTA for which we can bound the coefficients of the filters. Our case study is the limited-angle X-ray transform and its application to limited-angle computed tomography (LA-CT). In particular, we prove that, in the case of LA-CT, the operations of upscaling, downscaling, and convolution, which characterize our \Psi DONet and most deep learning schemes, can be exactly determined by combining the convolutional nature of the limited-angle Xray transform and basic properties defining an orthogonal wavelet system. We test two different implementations of \Psi DONet on simulated data from limited-angle geometry, generated from the ellipse data set. Both implementations provide equally good and noteworthy preliminary results, showing the potential of the approach we propose and paving the way to applying the same idea to other convolutional operators which are \Psi DOs or Fourier integral operators