Accelerating coordinate descent in iterative reconstruction

Iterative coordinate descent (ICD) is an optimization strategy for iterative reconstruction that is sometimes considered incompatible with parallel compute architectures such as graphics processing units (GPUs). We present a series of modifications that render ICD compatible with GPUs and demonstrate the code on a diagnostic, helical CT dataset. Our reference code is an open-source package, FreeCT ICD, which requires several hours for convergence. Three modifications are used. First, as with our reference code FreeCT ICD, the reconstruction is performed on a rotating coordinate grid, enabling the use of a stored system matrix. Second, every other voxel in the z-is updated direction simultaneously, and the sinogram data is shuffled to coalesce memory access. This increases the parallelism available to the GPU. Third, NS voxels in the xy-plane are updated simultaneously. This introduces possible crosstalk between updated voxels, but because the interaction between non-adjacent voxels is small, small values of NS still converge effectively. We find NS = 16 enables faster reconstruction via greater parallelism, and NS = 256 remains stable but has no additional computational benefit. When tested on a pediatric dataset of size 736x16x14000 reconstructed to a matrix size of 512x512x128 on a single GPU, our implementation of ICD can converge within 10 HU RMS in less than 5 minutes. This suggests that ICD could be competitive with simultaneous update algorithms on modern, parallel compute architectures.