Super-resolution: a comprehensive survey <s> Maximum likelihood <s> This paper describes a Bayesian method for constructing a super-resolved surface model by combining information from a set of images of the given surface. We develop the theory and algorithms in detail for the 2-D reconstruction problem, appropriate for the case where all images are taken from roughly the same direction and under similar lighting conditions. We show the results of this 2-D reconstruction on Viking Martian data. These results show dramatic improvements in both spatial and gray-scale resolution. The Bayesian approach uses a neighbor correlation model as well as pixel data from the image set. Some extensions of this method are discussed, including 3-D surface reconstruction and the resolution of diffraction blurred images. <s> BIB001 </s> Super-resolution: a comprehensive survey <s> Maximum likelihood <s> Super-resolution reconstruction deals with the recovery of a single high-resolution image from a set of warped, blurred and decimated versions of it. Several algorithms were already proposed for the solution of this general problem. We concentrate on a special case where the warps are pure translations, the blur is space invariant and the same for all the images, and the noise is white. We exploit previous results to develop a new highly efficient super-resolution reconstruction algorithm for this case, which separates the treatment to de-blurring and measurements fusion. The fusion part is shown to be a non-iterative and very simple algorithm, preserving the optimality of the entire reconstruction process, in the maximum-likelihood sense. Simulations demonstrate the capabilities of the proposed algorithm. <s> BIB002 </s> Super-resolution: a comprehensive survey <s> Maximum likelihood <s> This paper develops a multi-frame image super-resolution approach from a Bayesian view-point by marginalizing over the unknown registration parameters relating the set of input low-resolution views. In Tipping and Bishop's Bayesian image super-resolution approach [16], the marginalization was over the super-resolution image, necessitating the use of an unfavorable image prior. By integrating over the registration parameters rather than the high-resolution image, our method allows for more realistic prior distributions, and also reduces the dimension of the integral considerably, removing the main computational bottleneck of the other algorithm. In addition to the motion model used by Tipping and Bishop, illumination components are introduced into the generative model, allowing us to handle changes in lighting as well as motion. We show results on real and synthetic datasets to illustrate the efficacy of this approach. <s> BIB003 </s> Super-resolution: a comprehensive survey <s> Maximum likelihood <s> An algorithm for video resolution enhancement is presented. The approach borrows from previous methods for still-image super- resolution, introducing modifications better suited for the characteristics specific to video domain problems. Each high-resolution (HR) frame is determined through a series of MMSE spatial interpolations based on the local features (statistics) of the frame. Cross-frame registration is estimated externally and the reconstruction algorithm does not limit the form of the motion model, unlike previous data-fusion/deconvolution approaches which have required motion models that do not alter the point-spread function (i.e., motion/blur commutability). This feature is made possible using a reverse motion model mapping the locations of desired HR pixels onto their corresponding locations in the observation frames. An ticipating the existence of registration error found in typical video sequences, the algorithm also provides an internal validation of the observation pixels, helping to reduce significant mis-registration artifacts. An arbitrary enhancement factor can be used, allowing an output at any desired resolution. Interpolation and deblurring are incorporated as a single MMSE filtering operation, providing a non-iterative one-step reconstruction process. Experimental results demonstrating the capabilities of the algorithm are made available. <s> BIB004 </s> Super-resolution: a comprehensive survey <s> Maximum likelihood <s> We provide a position-patch based face hallucination method using convex optimization. Recently, a novel position-patch based face hallucination method has been proposed to save computational time and achieve high-quality hallucinated results. This method has employed least square estimation to obtain the optimal weights for face hallucination. However, the least square estimation approach can provide biased solutions when the number of the training position-patches is much larger than the dimension of the patch. To overcome this problem, this letter proposes a new position-patch based face hallucination method which is based on convex optimization. Experimental results demonstrate that our method is very effective in producing high-quality hallucinated face images. <s> BIB005
Let us assume that the noise term in the imaging model given in Eq. (5) is a Gaussian noise with zero mean and variance σ . Given an estimate of the super-resolved image,f , the total probability of an observed LR image g k is BIB001 50, BIB002  BIB003  BIB004 BIB005 : and its log-likelihood function is: The ML solution BIB001 (Table 7) seeks a super-resolved image, f ML , which maximizes the log-likelihood of Eq. (32) for all observations: (33) which can be solved by: which results in: The ML solution of an SR problem, which is equivalent to the LS solution of the inverse problem of Eq. (4), is an illconditioned problem, meaning it is sensitive to small disturbances, such as noise or errors in the estimation of the imaging parameters. Furthermore, if the number of LR images is less than the square of the improvement factor, it is ill-posed as well. This means that there might not be a unique solution. To deal with these problems, there is needed some additional information to constrain the solution. Such information can be a priori knowledge about the desired image. The a priori term can prefer a specific solution over other solutions when the solution is not unique. The involvement of that a priori knowledge can convert the ML problem to a MAP problem, which is discussed in the next section. If the number of LR images over-determines the superresolved images, the results of ML and MAP are the same and since the computation of ML is easier, it is preferred over MAP. However, if the number of the LR images is insufficient for the determination of the super-resolved image, the involvement of a priori knowledge plays an important role and MAP outperforms ML BIB001 . Table 7 Reported probabilistic-based SR works