Techniques and systems are disclosed for estimating an unknown image from a plurality of cone-beam computed tomography (CBCT) image projections. The unknown image is estimated by solving for minima of an expression comprising a fidelity term that is a function of the plurality of image projections and a regularization term that is responsive to a sparsity of the CBCT image projections. The minima of the expression is iteratively estimated by calculating an image gradient of the function, determining a step size based on a based on a Barzilai-Borwein (BB) formulation and adjusting the minima estimate using the projected image gradient and a step size.