In response to the practical need for restoring images which are degraded by systems which are bilinear, this paper focuses on the development and application of tools required for this purpose. When the blurring phenomenon can be modeled by a shift-variant bilinear system, the data restoration problem can be most conveniently formulated as a special system of linear equations with nonnegative coefficients, whose solution is required to satisfy constraints like nonnegativity in addition to it being factorable with the factors having a certain characterizing property. Recursive techniques for restoration are first developed when the blurring system is either causal or weakly causal. It is shown how these recursive techniques when applied several times and the solutions superposed can, sometimes, be used to restore images degraded by noncausal blurs. Algorithms based on noniterative and iterative schemes are, subsequently, developed to tackle directly the noncausal blurs. Performances of the various algorithms when applied to noisy images are briefly compared.