Abstract—We describe and evaluate an algorithm for image reconstruction in 3D x-ray computed tomography. The proposed algorithm is similar to the class of projected gradient methods. The gradient descent for reducing the measurement misfit term is carried out using a stochastic gradient iteration and the gradient directions are weighted using weights suggested by parallel coordinate descent. In addition, to further improve the speed of the algorithm, at each iteration we minimize the cost function on a small subspace spanned by the direction of the current projected gradient and several previous update directions. We apply the proposed algorithm on simulated and real cone-beam projections and compare it with Fast Iterative ShrinkageThresholding Algorithm (FISTA).