Compressed sensing for reduction of noise and artefacts in direct PET image reconstruction

Image reconstruction in positron emission tomography (PET) can be performed using either direct or iterative methods. Direct reconstruction methods need a short reconstruction time. However, for data containing few counts, they often result in poor visual images with high noise and reconstruction artefacts. Iterative reconstruction methods such as ordered subset expectation maximization (OSEM) can lead to overestimation of activity in cold regions distorting quantitative analysis. The present work investigates the possibilities to reduce noise and reconstruction artefacts of direct reconstruction methods using compressed sensing (CS).

Raw data are generated either using Monte Carlo simulations using GATE or are taken from PET measurements with a Siemens Inveon small-animal PET scanner. The fully sampled dataset was reconstructed using filtered backprojection (FBP) and reduced in Fourier space by multiplication with an incoherently undersampled sampling pattern, followed by an additional reconstruction with CS. Different sampling patterns are used and an average of the reconstructions is taken. The images are compared to the results of an OSEM reconstruction and quantified using signal-to-noise ratio (SNR).

The application of the proposed CS post-processing technique clearly improves the image contrast. Dependent on the undersampling factor, noise and artefacts are reduced resulting in an SNR that is increased up to 3.4-fold. For short acquisition times with low count statistics the SNR of the CS reconstructed image exceeds the SNR of the OSEM reconstruction.

Especially for low count data, the proposed CS-based post-processing method applied to FBP reconstructed PET images enhances the image quality significantly.