Numerical filtering techniques for image enhancement in medical imaging computed tomographic reconstruction

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Cone-beam CT using 2D panel detectors is finding increasing application in medical imaging, image guidance etc. However, 2D detectors are more susceptible to noise from scattering radiation than detectors used in more traditional fan-beam CT (Pan et al., 2008). Feldkamp-Davis-Kress (FDK) filtered back-projection (Feldkamp et al., 1984) is one of the most efficient and most commonly used reconstruction algorithms (Wang et al., 2008, Hsieh et al., 2013). Part of the algorithm involves adjusting amplitudes of different image spatial frequency components by applying a suitable filter in Fourier space (Fourier-filter or "kernel").

Typically, clinical CT systems deal with image noise by modifying the Fourier-filter response to adjust the attenuation or enhancement of different frequency components in the image. This choice is a compromise between minimising image noise and maximising contrast of tissue boundaries, as attenuating high frequencies reduces the contrast of both noise and sharp boundaries.

Standard image filters and enhancements were tested and compared against novel image enhancement techniques developed for this project. The images utilised for testing included: the image 'Lenna' which could be accessed from the image archive https://sipi.usc.edu/database/database.php?volume=misc#top but has since been removed and projections of an anthropomorphic skull phantom which came packaged with the AAPM-endorsed OSCaR (the open-source cone-beam CT reconstruction tool for imaging research) software suite (Rezvani et al., 2007) accessed from https://www.cs.toronto.edu/~nrezvani/ OSCaR.html. These images were utilised unmodified or seeded with additional Poissonian noise via the Matlab program 'AddPoissonNoise'. Seeding with Poisson noise was to simulate CT projections taken at lower X-ray intensity.

All image filters and enhancements were implemented via 'Matlab'. Where applied to the image Lenna (with or without additional Poissonian noise) no further modification of the base image was necessary. For projections of the anthropomorphic skull phantom, prior to filtering or enhancement, pixel values were modified to represent cumulative attenuation values as per the equation for X-ray attenuation where projecting through an object I_θ(x′,y,z₁′)=exp[-2k(P_θf)(x′,y)]I_θ(x′,y,z₀′) [where (P_θf)(x′,y) is the cumulative attenuation value and I_θ(x′,y,z₁′) is the pixel value for a projection]. OSCaR was used to reconstruct from cumulative attenuation maps (both enhanced and not). Reconstructions from enhanced projections were compared with reconstructions from those not enhanced.

Qualitative assessment of image-quality (visual-inspection) and quantitative assessment of image-quality were used to analyse results. Computation of: the signal-to-noise ratio (SNR); contrast-to-noise ratio (CNR) of the CT reconstructions; peak signal-to-noise ratio (PSNR) and contrast-improvement-ratio (CIR) provided quantitative measures on image-quality. PSNR provided a relative measure of the total amount of noise within a CT reconstruction, whilst CIR quantified how much the contrast (over the entire CT reconstruction) had changed from the contrast of a reference image (provided by reconstructions from those projections not enhanced).

Application of novel image enhancement techniques developed for this project in enhancement of cumulative attenuation maps prior to reconstruction via FDK filtered backprojection yielded improvements in quality of CT reconstructions. Comparing CT reconstructions, the relative benefits of selective enhancement (prior to reconstruction) were more strongly-pronounced from projections seeded with Poisson noise.