Abstract

A Boltzmann machine can be used to invert a linear equation expressed as g = Hf + n. A common application of this process Is to recover an object distribution f from a data set g representing multiplexed views of the object, such as would be formed by coded-aperture or badly aberrated imaging systems H in the presence of noise n. The algorithm performs a search for an optimum solution and must consider a great many matrix-vector products during its execution. Because of the feedback properties of the algorithm, the machine can use products generated by analog optical systems to guide Its evolution and converge to a reasonably precise solution with much greater speed than when using more conventional methods of determining the matrix-vector products. With occasional intervention by a digital machine to measure accurately the state of the solution, the Boltzmann machine may use the analog generated products to ultimately generate a solution with the precision available In the digital machine. Using the symmetries in the matrices representing shift-invariant imaging systems, we constructed analog optical systems to generate the vector products necessary to reconstruct 64K pixel objects from 64K pixel data.

© 1987 Optical Society of America