Image Restoration for Shift Invariant Blurs-A Survey <s> Learning-Based Approach <s> We introduce a new approach to optimal image scaling called resolution synthesis (RS). In RS, the pixel being interpolated is first classified in the context of a window of neighboring pixels; and then the corresponding high-resolution pixels are obtained by filtering with coefficients that depend upon the classification. RS is based on a stochastic model explicitly reflecting the fact that pixels falls into different classes such as edges of different orientation and smooth textures. We present a simple derivation to show that RS generates the minimum mean-squared error (MMSE) estimate of the high-resolution image, given the low-resolution image. The parameters that specify the stochastic model must be estimated beforehand in a training procedure that we have formulated as an instance of the well-known expectation-maximization (EM) algorithm. We demonstrate that the model parameters generated during the training may be used to obtain superior results even for input images that were not used during the training. <s> BIB001 </s> Image Restoration for Shift Invariant Blurs-A Survey <s> Learning-Based Approach <s> Super-resolution (SR) restoration aims to solve the following problem: given a set of observed images, estimate an image at a higher resolution than is present in any of the individual images. Where the application of this technique differs in computer vision from other fields is in the variety and severity of the registration transformation between the images. In particular this transformation is generally unknown, and a significant component of solving the SR problem in computer vision is the estimation of the transformation. The transformation may have a simple parametric form, or it may be scene dependent and have to be estimated for every point. In either case the transformation is estimated directly and automatically from the images. We describe the two key components that are necessary for successful SR restoration: the accurate alignment or registration of the LR images and the formulation of an SR estimator that uses a generative image model together with a prior model of the super-resolved image itself. As with many other problems in computer vision, these different aspects are tackled in a robust, statistical framework. <s> BIB002 </s> Image Restoration for Shift Invariant Blurs-A Survey <s> Learning-Based Approach <s> We consider the class of iterative shrinkage-thresholding algorithms (ISTA) for solving linear inverse problems arising in signal/image processing. This class of methods, which can be viewed as an extension of the classical gradient algorithm, is attractive due to its simplicity and thus is adequate for solving large-scale problems even with dense matrix data. However, such methods are also known to converge quite slowly. In this paper we present a new fast iterative shrinkage-thresholding algorithm (FISTA) which preserves the computational simplicity of ISTA but with a global rate of convergence which is proven to be significantly better, both theoretically and practically. Initial promising numerical results for wavelet-based image deblurring demonstrate the capabilities of FISTA which is shown to be faster than ISTA by several orders of magnitude. <s> BIB003
It uses powerful class-specific priors than generic image priors BIB001 BIB002 . It is used for both high-level classes and lowlevel classes. Constraining Solution to a Subspace is a one of training-based approach. If the image to be restored belongs to a class and there is a set of training images f 1 ,f 2 .. f N from that class than image f can be represented in terms of the average image a and K basis vectors = [ 1 , K ]: (36) here e shows the contributions of the basis vectors. Vector e size is smaller than the total pixels in f. Vector e is calculated by taking the inner product with the basis vectors: (37) Basis vectors are selected such that the difference between the image f and its subspace representation is made as small as possible. The restoration problem can be formulated in terms of the representation vector e. Optimal representation vector for the regularized least squares approach is given by: BIB003 In this approach noise that is orthogonal to the subspace is automatically eliminated.