In general, the super resolutionmethod focuses on the problem of recovering the low resolution to highresolution image. That is using input image and super-resolution algorithms topredict high resolution image, and the output can be represent the downscaleversion of the high-resolution image: where Drepresents a downscale operator.

Since super-resolution is an ill-posedproblem, we need some powerful prior knowledge toconstrain it. Because given a , for calculate the , it has infinite way.Our algorithm focuses on the problem of recovering the low resolution facial imageto high resolution facial image, and rely on the external example based methodto solve it.

Using the method of predicting high-resolution patches, and thepredicted image patches are finally integrated into . 3.1 Local structure prior Super-resolution is atypical ill-posed problem in image processing. Therefore, the problem need to be solved under someconstraints and the strength of the constraint will affect the quality of thetarget high-resolution image. In solving this problem of front human face imageresolution, the similarity of the front human face image can be used togenerate the constraint.

Through a series of imageprocessing steps to normalize, equalize, eye alignment and crop the front faceimages, we can ensure that for any , can find and at the same position has same features for alltraining images. 3.2 Data generation First, for the generate theinput image . To get a more blurred input image, we selectan image (Ground truth) and using the Nearest Neighbor method to down scale 4times, and then using the Nearest Neighbor method upscale 2 times (In general,the super resolution methods are used BICUBIC downscale 2 times). The reason is thatthe general downscale 2 times, the results of the prediction image and thegeneral interpolation algorithm, there is little difference in effect, so it isdifficult to show the performance of its algorithm.

For generating high frequency image and highfrequency patch , where – and = – . A two-dimensional image can be decomposed into different frequencycomponents. The low-frequency components describe a wide range of information,while the high – frequency components describe the specific details. It’s alsofor this reason that we want to get target high-resolution image by predictinghigh-frequency image patches .Therefore, we can establishthe relationship through the and F to restore the , and each F will change according to the patchlocation. 3.3 Eyealignment For input image that are not pre-processed by the eye alignment, theresult will have artifacts, as shown in Fig 2.

The reason is all used databaseimages are collated by eye alignment, so we need do the same preprocessing ofthe input image. The Fig 3 shows the we used database which collated by eyealignment.Weuse Viola-Jones face detection algorithm 29,which can help us find out the location of the eye.

For the Viola-Jones facedetection algorithm, the basic principle is to learn a classifier throughtraining set, and then slide it in the test image with different scale windows.Make a classification of each scan to determine whether the current window isthe target to be detected. We can according to the coordinates of the eyes partto crop image size to get the input image. This part can be summarized inAlgorithm 1, and Fig. 4 shows the detail process. For the F, we canrepresent it by a liner mapping function in a linearregression: = where A will alsochange according to the patch location, in other words, each group of patches ( and its corresponded and ) has a different A?so we can express it by a locally weightedregression as follows: = Forweight w, we introduce the SRLSP’ s18 smooth weighting: where i represents the position ofpatch and ? is a smoothing parameter, is the squared Euclidean distance betweenthe and , whenthe distance is smaller, w is bigger.Afterregularization term was added to complete the final equation, Eq.

(4) canbe written as the following expression: = + (5) where? is the regularcoefficient,which can balance the regular term and , and theregularization term is the Frobenius norm (). We can get byEq. (5) and Eq. (2), but for getting , we need combine it with : Finally, a common restorationalgorithm strategy is used to average the overlappingprediction patches () to obtain .We have the same regression equation structure with SRLSP. The differenceis that, for predict single patch, in the SRLSP, they extract the pixels of thefixed position in the predicted high-resolution patch, then to combine it withthe pixels which in the corresponding input patch.

Our approach is to get thehigh-frequency patch from the regression equation and get the high-resolutionpatch in combination with the input patch ().