Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images

TLDR

The single‑image restoration field relies on maximum likelihood, maximum a posteriori, and projection‑onto‑convex‑sets methods, and superresolution seeks to recover a high‑resolution image from geometrically warped, blurred, noisy, and downsampled measurements. The paper proposes a unified methodology using ML, MAP, and POCS to address superresolution restoration. The authors model superresolution as an ML/MAP/POCS optimization problem, assume known blur, noise, resolution, and motion, and introduce a hybrid ML‑based method with non‑ellipsoid constraints that generalizes existing approaches and handles motionless measurements. The hybrid method converges to the unique optimal solution of the new optimization problem and, in simulations, outperforms conventional ML and POCS approaches.

Abstract

The three main tools in the single image restoration theory are the maximum likelihood (ML) estimator, the maximum a posteriori probability (MAP) estimator, and the set theoretic approach using projection onto convex sets (POCS). This paper utilizes the above known tools to propose a unified methodology toward the more complicated problem of superresolution restoration. In the superresolution restoration problem, an improved resolution image is restored from several geometrically warped, blurred, noisy and downsampled measured images. The superresolution restoration problem is modeled and analyzed from the ML, the MAP, and POCS points of view, yielding a generalization of the known superresolution restoration methods. The proposed restoration approach is general but assumes explicit knowledge of the linear space- and time-variant blur, the (additive Gaussian) noise, the different measured resolutions, and the (smooth) motion characteristics. A hybrid method combining the simplicity of the ML and the incorporation of nonellipsoid constraints is presented, giving improved restoration performance, compared with the ML and the POCS approaches. The hybrid method is shown to converge to the unique optimal solution of a new definition of the optimization problem. Superresolution restoration from motionless measurements is also discussed. Simulations demonstrate the power of the proposed methodology.