This thesis presents a new technique to randomly sample from the large datasets in linear order. Existing stochastic sampling methods work well but are limited to the small datasets. If existing stochastic sampling methods are implemented for large datasets, thrashing results, wherein the Operating System will spend most of its time swapping the pages of memory rather than executing instructions.

We make two contributions to our research. First, we derive explicit formulas that minimize the stochastic sampling time and generate a higher quality of the output images at the same time. Second, we analyze the new algorithm in the context of visual quality, memory usage, and performance. The results of our analysis show that this technique is competitive with other stochastic sampling methods while avoiding thrashing and using computer memory more efficiently.