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Exact multichannel blind image restoration

Liu and Xu (see ibid., vol.43, no.11, p.2714-23, 1995) proposed a blind symbol estimation algorithm in digital communications. If all the channels are linear time-invariant finite impulse response (LTI FIR) filters, this algorithm can estimate symbols exactly when the channels and the input symbols satisfy some loose restrictions. We extend this algorithm to two dimensions, and in particular, to multichannel (noise-free) blind image restoration. Assuming linear FIR blur functions, given at least three blurred versions of the same image, and loose restrictions (different from those of Liu and Xu) on the original image and on the blur functions, the original image can be exactly recovered, up to a scalar multiplier.