Adaptive Dictionary Learning In Sparse Gradient Domain For CT Reconstruction

Owing to the advantage that CT can accurately, intuitively display the the interiorinformation of object, CT technology has received extensive attention and been appliedto various fields since the first CT was invented. How to improve the scanning speedand reduce the radiation dose to specimen has been a focus of research in CT domain.An effective way is to reduce the number of projections for reconstruction or usessparse projection. However, the traditional methods of CT image reconstruction willcause serious image distortion, artifacts and low signal to noise ratio when theprojections are sparse because of their inherent limitations. Fortunately, the theory ofcompressed sensing proposed in2006proved that we can use far fewer sampling datathan the Nyquist sampling theory to get an accurate reconstruction, which provides thepossibility to reconstruct image when the projections are sparse.Based on compressed sensing theory, this paper proposes a novel gradient baseddictionary learning method for CT reconstruction(GradDL-CT). It applies thegradient based dictionary learning method for CT reconstruction, uses adaptivedictionary learning method to effectivly reduse the drawbacks of the populartotalvariation (TV) regularization, selecets the sparser gradient based training samplesinstead of the pixel based. Compared to the image itself, it is sparser in the gradientdomain. Therefore, we can obtain sparser representation to learn dictionary ingradient domain than the image itself. The improvement of the sparsity of trainingsamples can improve the accuracy and robustness of the learning dictionary to someextent, then we can obtain reconstruction with more accurace.The main idea of the GradDL-CT method is that we firstly train dictionariesfrom the horizontal and vertical gradients of the image respectively, and thenreconstruct the desired image using the sparse representations of both derivatives,exploiting gradient magnitude image sparsity for reduction in the number ofprojections or the X-ray dose. According to the experimental results, usingGradDL-CT algorithm can obtain a more accurate reconstruction even through theprojections are incomplete.