Restoring a clear image from a single motion-blurred
image due to camera shake has long been a challenging
problem in digital imaging. Existing blind deblurring techniques
either only remove simple motion blurring, or need
user interactions to work on more complex cases. In this
paper, we present an approach to remove motion blurring
from a single image by formulating the blind blurring as a
new joint optimization problem, which simultaneously maximizes
the sparsity of the blur kernel and the sparsity of the
clear image under certain suitable redundant tight frame
systems (curvelet system for kernels and framelet system
for images). Without requiring any prior information of
the blur kernel as the input, our proposed approach is able
to recover high-quality images from given blurred images.
Furthermore, the new sparsity constraints under tight frame
systems enable the application of a fast algorithm called linearized
Bregman iteration to efficiently solve the proposed
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