Quantitative Image Reconstruction Methods for Low Signal-To-Noise Ratio Emission Tomography

Novel internal radionuclide therapies such as radioembolization (RE) with Y-90 loaded microspheres and targeted therapies labeled with Lu-177 offer a unique promise for personalized treatment of cancer because imaging-based pre-treatment dosimetry assessment can be used to determine administered activities, which deliver tumoricidal absorbed doses to lesions while sparing critical organs. At present, however, such therapies are administered with fixed or empiric activities with little or no dosimetry planning. The main reason for lack of dosimetry guided personalized treatment in radionuclide therapies is the challenges and impracticality of quantitative emission tomography imaging and the lack of well established dose-effect relationships, potentially due to inaccuracies in quantitative imaging. While radionuclides for therapy have been chosen for their attractive characteristics for cancer treatment, their suitability for emission tomography imaging is less than ideal. For example, imaging of the almost pure beta emitter, Y-90, involves SPECT via bremsstrahlung photons that have a low and tissue dependent yield or PET via a very low abundance positron emission (32 out of 1 million decays) that leads to a very low true coincidence-rate in the presence of high singles events from bremsstrahlung photons. Lu-177 emits gamma-rays suitable for SPECT, but they are low in intensity (113 keV: 6%, 208 keV: 10%), and only the higher energy emission is generally used because of the large downscatter component associated with the lower energy gamma-ray. The main aim of the research in this thesis is to improve accuracy of quantitative PET and SPECT imaging of therapy radionuclides for dosimetry applications. Although PET is generally considered as superior to SPECT for quantitative imaging, PET imaging of `non-pure' positron emitters can be complex. We focus on quantitative SPECT and PET imaging of two widely used therapy radionuclides, Lu-177 and Y-90, that have challenges associated with low count-rates. The long term goal of our work is to apply the methods we develop to patient imaging for dosimetry based planning to optimize the treatment either before therapy or after each cycle of therapy. For Y-90 PET/CT, we developed an image reconstruction formulation that relaxes the conventional image-domain nonnegativity constraint by instead imposing a positivity constraint on the predicted measurement mean that demonstrated improved quantification in simulated patient studies. For Y-90 SPECT/CT, we propose a new SPECT/CT reconstruction formulation including tissue dependent probabilities for bremsstrahlung generation in the system matrix. In addition to above mentioned quantitative image reconstruction methods specifically developed for each modality in Y-90 imaging, we propose a general image reconstruction method using trained regularizer for low-count PET and SPECT that we test on Y-90 and Lu-177 imaging. Our approach starts with the raw projection data and utilizes trained networks in the iterative image formation process. Specifically, we take a mathematics-based approach where we include convolutional neural networks within the iterative reconstruction process arising from an optimization problem. We further extend the trained regularization method by using anatomical side information. The trained regularizer incorporates the anatomical information using the segmentation mask generated by a trained segmentation network where its input is the co-registered CT image. Overall, the emission tomography methods we have proposed in this work are expected to enhance low-count PET and SPECT imaging of therapy radionuclides in patient studies, which will have value in establishing dose – response relationships and developing imaging based dosimetry guided treatment planning strategies in the future.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155171/1/hongki_1.pd

Mismatched Sparse Denoiser Requires Overestimating the Support Length

A well-known result states that, without noise, it is better to overestimate the support of a sparse signal, since, if the estimated support includes the true support, the reconstruction is perfect. In this paper, we investigate whether this result holds also in the presence of noise. First, we derive the covariance matrix of the signal estimate when the observation matrix is Gaussian, generalizing existing results. Then, we show that, even in the noisy case, overestimating the support length is the preferred solution, as the error incurred by missing some signal components dominates the overall error variance. Finally, an upper bound of the estimated support length is provided to avoid excessive noise amplification