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.

In this paper we propose a novel technique for superresolution imaging of a scene from observations at different zooms. Given a sequence of images with different zoom factors of a static scene, the problem is to obtain a picture of the entire scene at a resolution corresponding to the most zoomed image in the scene. We model the super-resolution image as a Markov random field (MRF) and a maximum a posteriori estimation method is used to derive a cost function which is then optimized to recover the high resolution field. Since there is no relative motion between the scene and the camera, as is the case with most of the superresolution techniques, we do away with the correspondence problem.

In this paper, we examine the theory of motion-free superresolution by formulating the problem in the Discrete Time Fourier Transform (DTFT) and the Discrete Fourier Transform (DFT) domain. Our approach provides some new insights into how aliasing and blurring can effect exact reconstruction of the superresolved image. For ease of understanding, the analysis, is initially carried out in the 1-D domain and then extended to the 2-D domain.

In this work, we address the task of enhancing the spatial resolution of video sequences, known as super-resolution. Specifically, we consider the problem of superresolving a human face video by a very high (16) zoom factor. Inspired by recent literature on hallucination and example-based learning, we formulate this task using a graphical model that encodes 1) spatio-temporal consistencies, and 2) image formation & degradation processes. A video database of facial expressions is used to learn a domain-specific prior for high-resolution videos. The problem is now one of probabilistic inference, in which we aim to find the high resolution video that best satisfies the constraints expressed through the graphical model. Traditional approaches to this problem using video data first estimate the relative motion between frames and then compensate for it, resulting effectively in multiple measurements of the scene. Our use of time is rather direct: We define data structures that span multiple consecutive frames, enriching our feature vectors with a temporal signature. We then exploit these signatures to find consistent solutions over time. We present