We denoised computed tomography (CT) imagery using a novel framework. This approach allows methods optimized for white noise to be used for signal-dependent noise present in low-dose CT imagery. Lowering the dose of x-rays results in an increase in quantum noise. We denoised an image independently several times using different parameters, then we selected pixels from those denoised images to form a final composite image. We compared results using a block-matching collaborative approach and a nonlocal means algorithm, but in principle other methods could work within this framework as well. The proposed framework improved denoising results in CT imagery when compared to not using the framework.