Computed Tomography Reconstruction from Undersampled Data: An Application to Biomedical Imaging

In computed tomography, there is often a need to reduce the amount of radiation used due to its potential to alter living tissue properties, especially in the patient or in vivo samples. To achieve this reduction, a method of measuring objects through sparse sampling can be employed. However, in mathematics, this problem leads to an ill-posed inverse problem due to limited measurement data. To address this issue, a regularization method is proposed, where the constraint for a regularized solution is enforced by utilizing Daubechies wavelet expansion coefficients. In this work, the algorithm is iteratively computed, employing a soft-thresholding operation for the coefficients, with the thresholding parameter automatically selected. For the purpose of biomedical imaging, we propose incorporating prior knowledge of the thresholding parameter value based on a biological object. The method is tested on simulated data using the chest phantom and real data obtained from the ladybug X-ray measurements.