L1-norm based regularization for a non linear imaging model tomography

Digital tomosynthesis is a technique that allows the reconstruction of any slice of a 3D object thanks to a certain number of 2D projections. The mathematical model for tomosynthesis was simplified until 2010. X-ray beam was considered to be monoenergetic and the object to be made up of one material. In this paper we consider the multimaterial polyenergetic model. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. Inverse problems requires a regularization in order to be stabilized and solved. In this paper we consider two types of regularization: the first based on the L1-Norm of the solution and the second based on the L1-Norm of the gradient of the solution (Total Variation). We'll, then, solve the regularized problem using two iterative methods: the Gradient method and a Non Linear Hybrid Conjugate Gradient method. La Tomosintesi Digitale è una tecnica in grado di ricostruire un qualsiasi numero di sezioni di un oggetto tridimenionale partendo da un insieme di proiezioni 2D. Fino al 2010 il modello matematico alla base della tomosintesi veniva semplificato. Il fascio di raggi X veniva considerato monoenergetico e l’oggetto composto di un solo materiale. In questo lavoro considereremo il modello polienergetico e multimateriale. Il modello polienergetico richiede la soluzione di un problema inverso di grandi dimensioni, la cui risoluzione è molto più complessa del problema ottenuto dal modello monoenergetico lineare. I problemi inversi richiedono un regolarizzazione per essere stabilizzati e risolti. Noi consideriamo due tipi di regolarizzazione: la prima basata sulla Norma L1 della soluzione e la seconda sulla Norma L1 del gradiente della soluzione (Variazione Totale). Risolveremo, poi, il problema regolarizzato utilizzando due metodi iterativi: Il metodo del Gradiente e un metodo del Gradiente Coniugato Non Lineare Ibrido

High-Resolution Quantitative Cone-Beam Computed Tomography: Systems, Modeling, and Analysis for Improved Musculoskeletal Imaging

This dissertation applies accurate models of imaging physics, new high-resolution imaging hardware, and novel image analysis techniques to benefit quantitative applications of x-ray CT in in vivo assessment of bone health. We pursue three Aims: 1. Characterization of macroscopic joint space morphology, 2. Estimation of bone mineral density (BMD), and 3. Visualization of bone microstructure. This work contributes to the development of extremity cone-beam CT (CBCT), a compact system for musculoskeletal (MSK) imaging. Joint space morphology is characterized by a model which draws an analogy between the bones of a joint and the plates of a capacitor. Virtual electric field lines connecting the two surfaces of the joint are computed as a surrogate measure of joint space width, creating a rich, non-degenerate, adaptive map of the joint space. We showed that by using such maps, a classifier can outperform radiologist measurements at identifying osteoarthritic patients in a set of CBCT scans. Quantitative BMD accuracy is achieved by combining a polyenergetic model-based iterative reconstruction (MBIR) method with fast Monte Carlo (MC) scatter estimation. On a benchtop system emulating extremity CBCT, we validated BMD accuracy and reproducibility via a series of phantom studies involving inserts of known mineral concentrations and a cadaver specimen. High-resolution imaging is achieved using a complementary metal-oxide semiconductor (CMOS)-based x-ray detector featuring small pixel size and low readout noise. A cascaded systems model was used to performed task-based optimization to determine optimal detector scintillator thickness in nominal extremity CBCT imaging conditions. We validated the performance of a prototype scanner incorporating our optimization result. Strong correlation was found between bone microstructure metrics obtained from the prototype scanner and µCT gold standard for trabecular bone samples from a cadaver ulna. Additionally, we devised a multiresolution reconstruction scheme allowing fast MBIR to be applied to large, high-resolution projection data. To model the full scanned volume in the reconstruction forward model, regions outside a finely sampled region-of-interest (ROI) are downsampled, reducing runtime and cutting memory requirements while maintaining image quality in the ROI

Mammographic density. Measurement of mammographic density

Mammographic density has been strongly associated with increased risk of breast cancer. Furthermore, density is inversely correlated with the accuracy of mammography and, therefore, a measurement of density conveys information about the difficulty of detecting cancer in a mammogram. Initial methods for assessing mammographic density were entirely subjective and qualitative; however, in the past few years methods have been developed to provide more objective and quantitative density measurements. Research is now underway to create and validate techniques for volumetric measurement of density. It is also possible to measure breast density with other imaging modalities, such as ultrasound and MRI, which do not require the use of ionizing radiation and may, therefore, be more suitable for use in young women or where it is desirable to perform measurements more frequently. In this article, the techniques for measurement of density are reviewed and some consideration is given to their strengths and limitations