Fluence estimation by deconvolution via l1-norm minimization

Advances in radiotherapy irradiation techniques have led to very complex treatments requiring for a more stringent control. The dosimetric properties of electronic portal imaging devices (EPID) encouraged their use for treatment verification. Two main approaches have been proposed: the forward approach, where measured portal dose images are compared to predicted dose images and the backward approach, where EPID images are used to estimate the dose delivered to the patient. Both approaches need EPID images to be converted into a fluence distribution by deconvolution. However, deconvolution is an ill-posed problem which is very sensitive to small variations on input data. This study presents the application of a deconvolution method based on l1-norm minimization; this is a method known for being very stable while working with noisy data. The algorithm was first evaluated on synthetic images with different noise levels, the results were satisfactory. Deconvolution algorithm was then applied to experimental portal images; the required EPID response kernel and energy fluence images were computed by Monte-Carlo calculation, accelerator treatment head and EPID models had already been commissioned in a previous work. The obtained fluence images were in good agreement with simulated fluence images. This deconvolution algorithm may be generalized to an inverse problem with a general operator, where image formation is not longer modeled by a convolution but by a linear operation that might be seen as a position-dependent convolution. Moreover, this procedure would be detector independent and could be used for any detector type provided its response function is known.