关键词: 压缩感知, 定步长, 锥束CT, 图像重建

Abstract: To solve the problem of image reconstruction of incomplete projection data from cone-beam CT, a fast cone-beam CT reconstruction algorithm was proposed. In this work, the cone-beam CT reconstruction problem was reduced to an unconstrained optimization problem of minimizing an objective function which included a squared error term combined with a sparseness-inducing regularization term. The Lipschitz continuity of the objective function was analyzed and the Lipschitz constant was estimated based on its definition. The gradient descent step-size was calculated by the Lipschitz constant and the reconstructed image was updated by gradient method. Finally simultaneous algebraic reconstruction technique was used to reconstruct image from limited-angle projections and to meet the constraint of the projection data. An adaptive step-size technique was accommodated as so to accelerate the convergence of proposed algorithm. Simulation with noiseless Shepp-Logan shows: In comparison with simultaneous algebraic reconstruction technique, adaptive steepest descent-projection onto convex sets algorithm and gradient-projection Barzilari-Borwein algorithm, the proposed algorithm has higher SNR (Signal-to-Noise Ratio) by 13.7728dB, 12.8205dB, and 7.3580dB respectively. The algorithm has better performance in convergence speed and reconstruction accuracy, and can greatly improve the quality of images reconstructed from few projection data.

Key words: compressed sensing, fixed stepsize, cone beam CT, image reconstruction