In general, the super resolution

method focuses on the problem of recovering the low resolution to high

resolution image. That is using input image and super-resolution algorithms to

predict high resolution image, and the output can be represent the downscale

version of the high-resolution image:

where D

represents a downscale operator. Since super-resolution is an ill-posed

problem, we need some powerful prior knowledge to

constrain it. Because given a , for calculate the , it has infinite way.

Our algorithm focuses on the problem of recovering the low resolution facial image

to high resolution facial image, and rely on the external example based method

to solve it. Using the method of predicting high-resolution patches, and the

predicted image patches are finally integrated into .

3.1 Local structure prior

Super-resolution is a

typical ill-posed problem in image processing. Therefore, the problem need to be solved under some

constraints and the strength of the constraint will affect the quality of the

target high-resolution image. In solving this problem of front human face image

resolution, the similarity of the front human face image can be used to

generate the constraint.

Through a series of image

processing steps to normalize, equalize, eye alignment and crop the front face

images, we can ensure that for any , can find

and at the same position has same features for all

training images.

3.2 Data generation

First, for the generate the

input image . To get a more blurred input image, we select

an image (Ground truth) and using the Nearest Neighbor method to down scale 4

times, 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 that

the general downscale 2 times, the results of the prediction image and the

general interpolation algorithm, there is little difference in effect, so it is

difficult to show the performance of its algorithm. For generating high frequency image and high

frequency patch , where – and = – . A two-dimensional image can be decomposed into different frequency

components. The low-frequency components describe a wide range of information,

while the high – frequency components describe the specific details. It’s also

for this reason that we want to get target high-resolution image by predicting

high-frequency image patches .

Therefore, we can establish

the relationship through the and F to restore the , and each F will change according to the patch

location.

3.3 Eye

alignment

For input image that are not pre-processed by the eye alignment, the

result will have artifacts, as shown in Fig 2. The reason is all used database

images are collated by eye alignment, so we need do the same preprocessing of

the input image. The Fig 3 shows the we used database which collated by eye

alignment.We

use Viola-Jones face detection algorithm 29,

which can help us find out the location of the eye. For the Viola-Jones face

detection algorithm, the basic principle is to learn a classifier through

training 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 is

the target to be detected. We can according to the coordinates of the eyes part

to crop image size to get the input image. This part can be summarized in

Algorithm 1, and Fig. 4 shows the detail process.

For the F, we can

represent it by a liner mapping function in a linear

regression:

=

where A will also

change 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 weighted

regression as follows:

=

For

weight w, we introduce the SRLSP’ s

18 smooth weighting:

where i represents the position of

patch and ? is a smoothing parameter, is the squared Euclidean distance between

the and , when

the distance is smaller, w is bigger.

After

regularization term was added to complete the final equation, Eq. (4) can

be written as the following expression:

= + (5)

where

? is the regular

coefficient,

which can balance the regular term and , and the

regularization term is the Frobenius norm ().

We can get by

Eq. (5) and Eq. (2), but for getting , we need combine it with :

Finally, a common restoration

algorithm strategy is used to average the overlapping

prediction patches () to obtain .

We have the same regression equation structure with SRLSP. The difference

is that, for predict single patch, in the SRLSP, they extract the pixels of the

fixed position in the predicted high-resolution patch, then to combine it with

the pixels which in the corresponding input patch. Our approach is to get the

high-frequency patch from the regression equation and get the high-resolution

patch in combination with the input patch ().