An iterative reconstruction algorithm without system matrix for EPR imaging.

Electron paramagnetic resonance (EPR) imaging is an advanced oxygen imaging modality for oxygen-image guided radiation. The iterative reconstruction algorithm is the research hot-point in image reconstruction for EPR imaging (EPRI) for this type of algorithm may incorporate image-prior information to construct advanced optimization model to achieve accurate reconstruction from sparse-view projections and/or noisy projections. However, the system matrix in the iterative algorithm needs complicated calculation and needs huge memory-space if it is stored in memory. In this work, we propose an iterative reconstruction algorithm without system matrix for EPRI to simplify the whole iterative reconstruction process. The function of the system matrix is to calculate the projections, whereas the function of the transpose of the system matrix is to perform backprojection. The existing projection and backprojection methods are all based on the configuration that the imaged-object remains stationary and the scanning device rotates. Here, we implement the projection and backprojection operations by fixing the scanning device and rotating the object. Thus, the core algorithm is only the commonly-used image-rotation algorithm, while the calculation and store of the system matrix are avoided. Based on the idea of image rotation, we design a specific iterative reconstruction algorithm for EPRI, total variation constrained data divergence minimization (TVcDM) algorithm without system matrix, and named it as image-rotation based TVcDM (R-TVcDM). Through a series of comparisons with the original TVcDM via real projection data, we find that the proposed algorithm may achieve similar reconstruction accuracy with the original one. But it avoids the complicated calculation and store of the system matrix. The insights gained in this work may be also applied to other imaging modalities, for example computed tomography and positron emission tomography.