Inside standard and hyperspectral low-dose CT variational imaging: parameter identification and material decomposition

The main contribution of this thesis is the proposal of novel strategies for the selection of parameters arising in variational models employed for the solution of inverse problems with data corrupted by Poisson noise. In light of the importance of using a significantly small dose of X-rays in Computed Tomography (CT), and its need of using advanced techniques to reconstruct the objects due to the high level of noise in the data, we will focus on parameter selection principles especially for low photon-counts, i.e. low dose Computed Tomography. For completeness, since such strategies can be adopted for various scenarios where the noise in the data typically follows a Poisson distribution, we will show their performance for other applications such as photography, astronomical and microscopy imaging. More specifically, in the first part of the thesis we will focus on low dose CT data corrupted only by Poisson noise by extending automatic selection strategies designed for Gaussian noise and improving the few existing ones for Poisson. The new approaches will show to outperform the state-of-the-art competitors especially in the low-counting regime. Moreover, we will propose to extend the best performing strategy to the hard task of multi-parameter selection showing promising results. Finally, in the last part of the thesis, we will introduce the problem of material decomposition for hyperspectral CT, which data encodes information of how different materials in the target attenuate X-rays in different ways according to the specific energy. We will conduct a preliminary comparative study to obtain accurate material decomposition starting from few noisy projection data.

CT perfusion image processing: analysis of liver tumors

Perfusion CT imaging of the liver has potential to improve evaluation of tumour angiogenesis. Quantitative parameters can be obtained applying mathematical models to Time Attenuation Curve (TAC). However, there are still some difficulties for an accurate quantification of perfusion parameters due, for example, to algorithms employed, to mathematical model, to patient’s weight and cardiac output and to the acquisition system. In this thesis, new parameters and alternative methodologies about liver perfusion CT are presented in order to investigate the cause of variability of this technique. Firstly analysis were made to assess the variability related to the mathematical model used to compute arterial Blood Flow (BFa) values. Results were obtained implementing algorithms based on “ maximum slope method” and “Dual input one compartment model” . Statistical analysis on simulated data demonstrated that the two methods are not interchangeable. Anyway slope method is always applicable in clinical context. Then variability related to TAC processing in the application of slope method is analyzed. Results compared with manual selection allow to identify the best automatic algorithm to compute BFa. The consistency of a Standardized Perfusion Index (SPV) was evaluated and a simplified calibration procedure was proposed. At the end the quantitative value of perfusion map was analyzed. ROI approach and map approach provide related values of BFa and this means that pixel by pixel algorithm give reliable quantitative results. Also in pixel by pixel approach slope method give better results. In conclusion the development of new automatic algorithms for a consistent computation of BFa and the analysis and definition of simplified technique to compute SPV parameter, represent an improvement in the field of liver perfusion CT analysis.