Compact MIMO systems often suffer from degraded channel capacity due to spatial correlation. To overcome this issue, we propose a formulation for the channel capacity of a compact MIMO system that directly links it to the geometry of a pixelated surface embedded into the MIMO system. This formulation allows us to maximize the channel capacity of the MIMO system and straightforwardly obtain the optimum geometry for the pixelated surface that reduces spatial correlation. The key step in obtaining the formulation is to link the pixelated surface geometry to an impedance matrix that allows us to obtain an expression for the systems channel capacity. The formulation is general and can be applied to a wide variety of MIMO antenna systems and geometries. To demonstrate the versatility of the approach, we include a design for a compact 4-port planar inverted-F antenna (PIFA) array integrated with a pixelated surface. Simulations and experiments are provided to evaluate the performance of the compact MIMO system with and without optimization of the surface. It is shown that optimizing the geometry of the pixelated surface can increase channel capacity by 13% and energy efficiency by 19.9% compared to the system without optimization. The importance of the approach is that it provides a link between communication and electromagnetic formulations of MIMO antenna systems.