Blind identification of multichannel FIR blurs and perfect image restoration

Despite its practical importance in image processing and computer vision, blind blur identification and blind image restoration have so far been addressed under restrictive assumptions such as all-pole stationary image models blurred by zero- or minimum-phase point-spread functions. Relying upon diversity (availability of a 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 nonblind setups), the inaccessible input image is allowed to be deterministic or random and of unknown color or distribution. With the blurs satisfying a certain co-primeness condition in addition, we establish existence and uniqueness results which guarantee that single-input/multiple-output FIR blurred images can be restored blindly, though perfectly in the absence of noise, using linear FIR filters. Results of simulations employing the blind order determination, blind blur identification, and blind image restoration algorithms are presented. When the SNR is high, direct image restoration is found to yield better results than indirect image restoration which employs the estimated blurs. In low SNR, indirect image restoration performs well while the direct restoration results vary with the delay but improve with larger equalizer orders.