Reducing streak artifacts in computed tomography via sparse representation in coupled dictionaries

Purpose: Reducing the number of acquired projections is a simple and efficient way to reduce the radiation dose in computed tomography (CT). Unfortunately, this results in streak artifacts in the reconstructed images that can significantly reduce their diagnostic value. This paper presents a novel algorithm for suppressing these artifacts in 3D CT. Methods: The proposed algorithm is based on the sparse representation of small blocks of 3D CT images in learned overcomplete dictionaries. It learns two dictionaries, the first dictionary ( D a ) is for artifact‐full images that have been reconstructed from a small number (approximately 100) of projections. The other dictionary ( D c ) is for clean artifact‐free images. The core idea behind the proposed algorithm is to relate the representation coefficients of an artifact‐full block in D a to the representation coefficients of the corresponding artifact‐free block in D c . The relation between these coefficients is modeled with a linear mapping. The two dictionaries and the linear relation between the coefficients are learned simultaneously from the training data. To remove the artifacts from a test image, small blocks are extracted from this image and their sparse representation is computed in D a . The linear map is then used to compute the corresponding coefficients in D c , which are then used to produce the artifact‐suppressed blocks. Results: The authors apply the proposed algorithm on real cone‐beam CT images. Their results show that the proposed algorithm can effectively suppress the artifacts and substantially improve the quality of the reconstructed images. The images produced by the proposed algorithm have a higher quality than the images reconstructed by the FDK algorithm from twice as many projections. Conclusions: The proposed sparsity‐based algorithm can be a valuable tool for postprocessing of CT images reconstructed from a small number of projections. Therefore, it has the potential to be an effective tool for low‐dose CT.