Coded aperture X-ray coherent scatter imaging is a novel modality for ascertaining the molecular structure of an object. Measurements from different spatial locations and spectral channels in the object are multiplexed through a radiopaque material (coded aperture) onto the detectors. Iterative algorithms such as penalized expectation maximization (EM) and fully separable spectrally-grouped edge-preserving reconstruction have been proposed to recover the spatially-dependent coherent scatter spectral image from the multiplexed measurements. Such image recovery methods fall into the category of domain decomposition methods since they recover independent pieces of the image at a time. Ordered subsets has also been utilized in conjunction with penalized EM to accelerate its convergence. Ordered subsets is a range decomposition method because it uses parts of the measurements at a time to recover the image. In this paper, we analyze domain and range decomposition methods as they apply to coded aperture X-ray coherent scatter imaging using a spectrally-grouped edge-preserving regularizer and discuss the implications of the increased availability of parallel computational architecture on the choice of decomposition methods. We present results of applying the decomposition methods on experimental coded aperture X-ray coherent scatter measurements. Based on the results, an underlying observation is that updating different parts of the image or using different parts of the measurements in parallel, decreases the rate of convergence, whereas using the parts sequentially can accelerate the rate of convergence.