Abstract
Rapid developments in photon-counting and energy-discriminating detectors have the potential to provide an additional spectral dimension to conventional x-ray grayscale imaging. Reconstructed spectroscopic tomographic data can be used to distinguish individual materials by characteristic absorption peaks. The acquired energy-binned data, however, suffer from low signal-to-noise ratio, acquisition artifacts, and frequently angular undersampled conditions. New regularized iterative reconstruction methods have the potential to produce higher quality images and since energy channels are mutually correlated it can be advantageous to exploit this additional knowledge. In this paper, we propose a novel method which jointly reconstructs all energy channels while imposing a strong structural correlation. The core of the proposed algorithm is to employ a variational framework of parallel level sets to encourage joint smoothing directions. In particular, the method selects reference channels from which to propagate structure in an adaptive and stochastic way while preferring channels with a high data signal-to-noise ratio. The method is compared with current state-of-the-art multi-channel reconstruction techniques including channel-wise total variation and correlative total nuclear variation regularization. Realistic simulation experiments demonstrate the performance improvements achievable by using correlative regularization methods.
Highlights
The general FISTA algorithm has been implemented in MATLAB with the time-consuming proximal operators to specify total variation (TV), total nuclear variation (TNV) and directional TV regularizer (dTV) regularizers respectively implemented in OpenMP/CUDA to accelerate computations
To further confirm the competitiveness of the proposed method, in figure 13 we present mass attenuation coefficients (MACs) plots for four materials reconstructed with the FBP, TV, TNV, and dTV-p methods
We presented a one possible approach to select a probability mass function (PMF), based on which the reference channel is selected for the dTV-p method
Summary
Conventional x-ray imaging entails a polychromatic x-ray source (i.e. a beam having a wide spectrum of energies) utilizing detectors that count photons without any energy discrimination This increases the intensity and photon count, but results in non-linear attenuation leading to ‘beam-hardening’ artifacts [1,2,3,4,5]. During propagation of a poly-energetic beam in matter, low-energy photons are absorbed more than high-energy photons resulting in a shift of the x-ray spectrum toward the higher energies This affects the assumed linearity of Beer’s law and biases the reconstructions with ‘beam hardening’ artifacts [4]. To this end the present work proposes a new correlative reconstruction method which addresses the low data SNR by encouraging joint structures across the channels
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