Blurs and perfect image restoration

Despite its practical importance in image processing and computer vision, blind blur identification and restoration has so far been addressed under restrictive assumptions such as all-pole stationary image models blurred by zero-or minimum-phase PSFs. Relying upon diversity (sufficient number of multiple blurred images), we develop blind FIR blur identification and order determination schemes. Apart from a minimal persistence of excitation condition (also present with non-blind setups), the inaccessible input is allowed to be deterministic or random and of unknown color or distribution. With the blurs also satisfying a certain co-primeness condition, we establish existence and uniqueness results which guarantee that single-input/multiple-output FIR blurred images can be restored perfectly but blindly using linear FIR filters. The resulting direct blind restoration filters by-pass the blur identification step and work well in higher SNRs. In lower SNRs better results are achieved by first identifying the blurs and then constructing the MMSE solution.