Space-variant deconvolution of Cerenkov light images acquired from a curved surface

Cerenkov photons are generated by high-energy radiation used in external beam radiation therapy (EBRT). This study expands upon the Cerenkov light dosimetry formula previously developed to relate an image of Cerenkov photons to the primary beam fluence. Extension of this formulation allows for deconvolution to be performed on images acquired from curved geometries.

The integral equation, which represented the formation of Cerenkov photon image from an incident high-energy photon beam, was expanded to allow for space-variance of the convolution kernel called as the Cerenkov scatter function (CSF). The GAMOS (Geant4-based Architecture for Medicine-Oriented Simulations) Monte Carlo (MC) particle simulation software was used to obtain the CSF for different incident beam angles. The image of a curved surface was first projected to a flat plane by using a perspective correction method. Then, the planar image was partitioned into small segments (or blocks), where a CSF corresponding to a specific beam incident angle was applied for deconvolution. The block size and the margin around the block were optimized by studying the effects of those parameters on the deconvolution accuracy for a test image. We evaluated three deconvolution techniques: Richardson-Lucy, Blind, and Total Variation minimization (TV/L2) algorithms, to select the most accurate method for the current applications.

Analysis of deconvolution algorithms showed that the TV/L2 method provided the most accurate solution to the deconvolution problem for Cerenkov imaging. Optimization of space-variant deconvolution parameters showed that including a margin that is at least 42.9% of the image width provided the most accurate product image. There was no optimal size for the deconvolution area and should be chosen based on the presence of unique CSF kernels within an image. Space-variant deconvolution improved measured field size in Cerenkov photon images by 7.37%, as compared with 1.74% by space-invariant deconvolution. Space-variant deconvolution improved measured penumbra by 99.3%, as compared with 76.7% by space-invariant deconvolution. Space-variant deconvolution introduced artifacts in flat regions of the beam. Artifacts were avoided through selective space-variant deconvolution in only the penumbra region.

Primary photon fluence distributions of a curved surface can be obtained by using space-variant deconvolution methods in Cerenkov light dosimetry. The TV/L2 algorithm is the best method for deconvolution of Cerenkov photon images from an open-field beam derived from either a flat or curved surface. The partition size chosen for space-variant deconvolution should be at least six times the full width at half maximum (FWHM) of the corresponding scatter kernel used in deconvolution. Space-variant deconvolution is necessary if the incident beam angle difference is larger than 6 $$ between regions of an image.