| Images may be degraded for many reasons. For example, out-of-focus optics produce blurred images while variations in electronic imaging components introduce noise. Reducing blur and noise in images is known as image restoration. Multichannel blind image restoration recovers an original image from several blurred versions without any knowledge of the blur functions. In this work, sufficient conditions for exact multichannel blind image restoration, up to a scalar ambiguity, are derived. However, the sufficient conditions are dependent on characteristics of the unknown original image and blur functions. From ideas in algebraic geometry, generically sufficient conditions are shown. Generically, the original image can be exactly restored if three blurred versions of the original image with sufficiently large size are available. In addition, alternative approaches for exact restoration are provided using optimization techniques.; Based on the developments for the exact restoration, two multichannel blind image restoration algorithms are proposed. They are extensions of blind multichannel one dimensional signal estimation algorithms to two dimensions. The implementation issues of both algorithms are then discussed. In noise-free cases, the proposed algorithms can exactly restore the original image. In noisy cases, the restored images obtained by these two algorithms are equal to each other. Furthermore, the connection among a restoration filter estimation algorithm and the proposed algorithms is presented. The effect of noise on the restored image is studied. Finally, numerous simulations are conducted to demonstrate the proposed algorithms. |
