Best Paper Award
Image Recovery by Decomposition with Component-wise Regularization
Shunsuke Ono , Takamichi Miyata , Isao Yamada , Katsunori Yamaoka
[Trans. Fundamentals., Vol. E95-A No.12, Dec. 2012]

Shunsuke Ono
Takamichi Miyata
Isao Yamada
Katsunori Yamaoka		  
　Image restoration, which pertains to the estimation of an unknown original image from a noisy degraded observation, is a fundamental task in many image processing applications such as digital camera imaging, medical imaging, astronomical imaging, and remote sensing. One effective approach to image restoration is non-smooth convex optimization, which has recently emerged as a powerful strategy that can exploit various underlying properties of images. In this approach, a restored image is characterized as a minimizer of a carefully designed convex objective function that involves a regularization term, for incorporating a priori knowledge on some underlying properties of images, and a data-fidelity term, for keeping estimates consistent with the given observation. However, for regularization, most of the existing methods based on convex optimization utilize smoothing priors that often fail to reconstruct well-textured regions, such as in the case of the widely-known total variation (TV) regularization.
　To overcome this situation, we first modeled the image to be estimated as the sum of three meaningful components; namely, smooth, edge, and texture components. We then treated the three components as components of a vector belonging to a product space of images. Second, using TV and two different frame transforms, we designed a convex objective function that promotes the underlying properties of each component and at the same time maintains data fidelity. Thus the simultaneous estimation of the three components was reduced into a convex optimization problem in the product space. Finally, the problem was reformulated by variable splitting, which led to an efficient algorithmic solution to the problem via the so-called alternating direction method of multipliers (ADMM).
　Experimental results demonstrate that the proposed method effectively restores the three meaningful components and is superior to state-of-the-art methods.
　As stated above, this paper proposes a novel and effective image restoration technique, which is well supported by clear and technically sound discussions. Accordingly, the paper is worthy of the IEICE Best Paper Award.

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