In a blurred image caused by defocus of a lens, the blurring kernel changes depending on the image position. The Discrete Wavelet transform is an adequate vehicle for resorting defocusing blur, because it enables a positional frequency representation. However, the Discrete Wavelet transform has shift-variance problem In this paper, we show that the shift-variance problem of the Wavelet transform affects the performance of restoration of defocusing blur, and that the shift invariant Wavelet transform improves the restoration of defocusing blur, using synthesized images. For restoring the defocusing blur, we assume that the blurring kernel of any position in a image can be obtained, as well as the noise level of a camera. We also show that the proposed restoring method can be applied to real images when we can use range data.
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