Tomographic 3D reconstruction through linear inversion for breast microwave imaging

In the present thesis we address the problem of detecting and localizing a small spherical target with characteristic electrical properties inside a volume of cylindrical shape, representing female breast, with MWI. One of the main works of this project is to properly extend the existing linear inversion algorithm from planar slice to volume reconstruction; results obtained, under the same conditions and experimental setup are reported for the two different approaches. Preliminar comparison and performance analysis of the reconstruction algorithms is performed via numerical simulations in a software-created environment: a single dipole antenna is used for illuminating the virtual breast phantom from different positions and, for each position, the corresponding scattered field value is registered. Collected data are then exploited in order to reconstruct the investigation domain, along with the scatterer position, in the form of image called pseudospectrum. During this process the tumor is modeled as a dielectric sphere of small radius and, for electromagnetic scattering purposes, it's treated as a point-like source. To improve the performance of reconstruction technique, we repeat the acquisition for a number of frequencies in a given range: the different pseudospectra, reconstructed from single frequency data, are incoherently combined with MUltiple SIgnal Classification (MUSIC) method which returns an overall enhanced image. We exploit multi-frequency approach to test the performance of 3D linear inversion reconstruction algorithm while varying the source position inside the phantom and the height of antenna plane. Analysis results and reconstructed images are then reported. Finally, we perform 3D reconstruction from experimental data gathered with the acquisition system in the microwave laboratory at DIFA, University of Bologna for a recently developed breast-phantom prototype; obtained pseudospectrum and performance analysis for the real model are reported.

From point cloud to HBIM: an integrated workflow for 3D reconstruction of heritage building with model accuracy evaluation

Modern society is now facing significant difficulties in attempting to preserve its architectural heritage. Numerous challenges arise consequently when it comes to documentation, preservation and restoration. Fortunately, new perspectives on architectural heritage are emerging owing to the rapid development of digitalization. Therefore, this presents new challenges for architects, restorers and specialists. Additionally, this has changed the way they approach the study of existing heritage, changing from conventional 2D drawings in response to the increasing requirement for 3D representations. Recently, Building Information Modelling for historic buildings (HBIM) has escalated as an emerging trend to interconnect geometrical and informational data. Currently, the latest 3D geomatics techniques based on 3D laser scanners with enhanced photogrammetry along with the continuous improvement in the BIM industry allow for an enhanced 3D digital reconstruction of historical and existing buildings. This research study aimed to develop an integrated workflow for the 3D digital reconstruction of heritage buildings starting from a point cloud. The Pieve of San Michele in Acerboli’s Church in Santarcangelo Di Romagna (6th century) served as the test bed. The point cloud was utilized as an essential referential to model the BIM geometry using Autodesk Revit® 2022. To validate the accuracy of the model, Deviation Analysis Method was employed using CloudCompare software to determine the degree of deviation between the HBIM model and the point cloud. The acquired findings showed a very promising outcome in the average distance between the HBIM model and the point cloud. The conducted approach in this study demonstrated the viability of producing a precise BIM geometry from point clouds.

Compressed sensing in digital tomosynthesis reconstruction

In this work we study a model for the breast image reconstruction in Digital Tomosynthesis, that is a non-invasive and non-destructive method for the three-dimensional visualization of the inner structures of an object, in which the data acquisition includes measuring a limited number of low-dose two-dimensional projections of an object by moving a detector and an X-ray tube around the object within a limited angular range. The problem of reconstructing 3D images from the projections provided in the Digital Tomosynthesis is an ill-posed inverse problem, that leads to a minimization problem with an object function that contains a data fitting term and a regularization term. The contribution of this thesis is to use the techniques of the compressed sensing, in particular replacing the standard least squares problem of data fitting with the problem of minimizing the 1-norm of the residuals, and using as regularization term the Total Variation (TV). We tested two different algorithms: a new alternating minimization algorithm (ADM), and a version of the more standard scaled projected gradient algorithm (SGP) that involves the 1-norm. We perform some experiments and analyse the performance of the two methods comparing relative errors, iterations number, times and the qualities of the reconstructed images. In conclusion we noticed that the use of the 1-norm and the Total Variation are valid tools in the formulation of the minimization problem for the image reconstruction resulting from Digital Tomosynthesis and the new algorithm ADM has reached a relative error comparable to a version of the classic algorithm SGP and proved best in speed and in the early appearance of the structures representing the masses.