1. A method of estimating an unknown image from a plurality of cone-beam computed tomography (CBCT) image projections, the method comprising: estimating the unknown image in a lower resolution having a plurality of image voxels by solving for a minima of a function comprising a fidelity term that is based on the plurality of image projections and a regularization term that is responsive to a sparsity of the CBCT image projections; and resampling the lower resolution estimation to a higher resolution for a second-level estimation of the unknown image; wherein the step of solving comprises: iteratively estimating the minima of the function by: calculating a gradient of the function for each image voxel of the plurality of image voxels in parallel; determining a first step size based on a Radon transform operator, a projected gradient of the fidelity term, and a gradient of the fidelity term at a first iteration; determining a second step size based on a Barzilai-Borwein (BB) formulation including approximating a second-order Hessian of the function by a scaled identity matrix at each iteration after the first iteration, wherein the determining is performed without using an iterative search; and adjusting the minima estimate using the fidelity term and the first step size for the first iteration and using the gradient and the second step size after the first iteration.