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Computed tomography (CT) is one of the most used imaging modalities for imaging both symptomatic and asymptomatic patients. However, because of the high demand for lower radiation dose during CT scans, the reconstructed image can suffer from noise and artifacts due to the trade-off between the image quality and the radiation dose. The purpose of this paper is to improve the image quality of quarter dose images and to select the best hyperparameters using the regular dose image as ground truth.We first generated the axially stacked two-dimensional sinograms from the multislice raw projections with flying focal spots using a single slice rebinning method, which is an axially approximate method to provide simple implementation and efficient memory usage. To improve the image quality, a cost function containing the Poisson log-likelihood and spatially encoded nonlocal penalty is proposed. Specifically, an ordered subsets separable quadratic surrogates (OS-SQS) method for the log-likelihood is exploited and the patch-based similarity constraint with a spatially variant factor is developed to reduce the noise significantly while preserving features. Furthermore, we applied the Nesterov's momentum method for acceleration and the diminishing number of subsets strategy for noise consistency. Fast nonlocal weight calculation is also utilized to reduce the computational cost.Datasets given by the Low Dose CT Grand Challenge were used for the validation, exploiting the training datasets with the regular and quarter dose data. The most important step in this paper was to fine-tune the hyperparameters to provide the best image for diagnosis. Using the regular dose filtered back-projection (FBP) image as ground truth, we could carefully select the hyperparameters by conducting a bias and standard deviation study, and we obtained the best images in a fixed number of iterations. We demonstrated that the proposed method with well selected hyperparameters improved the image quality using quarter dose data. The quarter dose proposed method was compared with the regular dose FBP, quarter dose FBP, and quarter dose l1-based 3-D TV method. We confirmed that the quarter dose proposed image was comparable to the regular dose FBP image and was better than images using other quarter dose methods. The reconstructed test images of the accreditation (ACR) CT phantom and 20 patients data were evaluated by radiologists at the Mayo clinic, and this method was awarded first place in the Low Dose CT Grand Challenge.We proposed the iterative CT reconstruction method using a spatially encoded nonlocal penalty and ordered subsets separable quadratic surrogates with the Nesterov's momentum and diminishing number of subsets. The results demonstrated that the proposed method with fine-tuned hyperparameters can significantly improve the image quality and provide accurate diagnostic features at quarter dose. The performance of the proposed method should be further improved for small lesions, and a more thorough evaluation using additional clinical data is required in the future.