This paper proposes a high-quality computed tomography (CT) image reconstruction method from low-dose X-ray projection data. A state-of-the-art method, proposed by Xu et al., exploits dictionary learning for image patches. This method generates an overcomplete dictionary from patches of standard-dose CT images and reconstructs low-dose CT images by minimizing the sum of a data fidelity and a regularization term based on sparse representations with the dictionary. However, this method does not take characteristics of each patch, such as textures or edges, into account. In this paper, we propose to classify all patches into several classes and utilize an individual dictionary with an individual regularization parameter for each class. Furthermore, for fast computation, we introduce the orthogonality to column vectors of each dictionary. Since similar patches are collected in the same cluster, accuracy degradation by the orthogonality hardly occurs. Our simulations show that the proposed method outperforms the state-of-the-art in terms of both accuracy and speed.

We propose a maximum likelihood estimation approach for the recovery of continuously-defined sparse signals from noisy measurements, in particular periodic sequences of Diracs, derivatives of Diracs and piecewise polynomials. The conventional approach for this problem is based on least-squares (a.k.a. annihilating filter method) and Cadzow denoising. It requires more measurements than the number of unknown parameters and mistakenly splits the derivatives of Diracs into several Diracs at different positions. Moreover, Cadzow denoising does not guarantee any optimality. The proposed approach based on maximum likelihood estimation solves all of these problems. Since the corresponding log-likelihood function is non-convex, we exploit the stochastic method called particle swarm optimization (PSO) to find the global solution. Simulation results confirm the effectiveness of the proposed approach, for a reasonable computational cost.