Image denoising in computed tomography using learned discriminative dictionaries

Abstract

Denoising of low-dose computed tomography (CT) images can substantially improve their diagnostic value. Learned overcomplete dictionaries have proved to be a powerful tool for this purpose. However, because the variability of the shape of features in a single CT image may be too high for a single dictionary to capture, previous studies have failed to exploit the true power of learned dictionaries for CT denoising. This study addresses this challenge by learning multiple dictionaries and using them to denoise CT images. Without loss of generality, we focus on the case where the CT image has two main parts with different structures. We jointly learn two dictionaries, one for each image part, such that each of the two dictionaries is very effective for representing patches from its corresponding image part but fails to effectively represent patches from the other part of the image. Dictionaries learned in this way will be able to effectively differentiate patches of the two image parts and denoise them. For denoising, we propose a soft segmentation strategy such that both dictionaries contribute to the denoised estimate of every patch in the image. We apply the proposed method on CT images with simulated Gaussian noise and also on low-dose CT images with realistic noise. Our results show that dictionaries learned with this approach are able to differentiate patches of structurally different parts of a CT image. In terms of denoising, this method achieves significantly better results than a method that learns two dictionaries independently and a method that learns only one dictionary. Our findings suggest that a single dictionary trained using the standard learning algorithms is unable to handle the large variety of structures that can be present in a CT image. Large improvements in denoising performance can be obtained if multiple dictionaries are learned for structurally different parts of the image. Further improvements can be achieved by training the dictionaries to differentiate patches that belong to the different image parts.