Achieving a realistic and high visual quality image is a crucial task in visual effect and movie industries. Numerous rendering features have been widely applied in movie and game applications, like global illumination, physically based lighting, realistic material and detailed geometry models. But the extra cost of applying these features is that the increment in the level of complexity. Instead of using brute-force rendering strategy, we propose to utilize matrix completion strategy to reduce the high computational burden of Monte Carlo rendering. Based on the proposed approach, the goal of this thesis is to provide efficient sampling and reconstruction techniques for image domain reconstruction, many lights problem and sub-pixel rendering. This will be achieved by exploiting characters in time, frequency or gradient domain, such as sparse property and low rank property. This thesis will outline methods of advanced sampling and reconstruction that can improve the efficiency of Monte Carlo rendering within a fixed budgets.