Limited-Angle X-Ray CT Reconstruction Using Image Gradient <i>ℓ</i>₀-Norm With Dictionary Learning

Abstract

Limited-angle X-ray computed tomography (CT) reconstruction is a typical ill-posed problem. To recover satisfied reconstructed images with limited-angle CT projections, prior information is usually introduced into image reconstruction, such as the piece-wise constant, nonlocal image similarity, and so on. To further improve the image quality for limited-angle CT reconstruction, the dictionary learning (DL) and image gradient ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm are combined into image reconstruction model, it can be called as ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> DL reconstruction technique. The advantages of ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> DL can be divided into two aspects. On one hand, the proposed ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> DL method can inherit the advantages of DL in image details preservation and features recovery by exploring an over-complete dictionary. On the other hand, the image gradient ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm minimization can further protect image edges and reduce shadow artifact. Both numerical simulation and preclinical mouse experiments are performed to validate and evaluate the outperformances of proposed ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> DL method by comparing with other state-of-the-art methods, such as total variation (TV) minimization and TV with low rank (TV + LR).