Digital image processing graphic image restoration task

One 、 Image degradation

         Compared with image enhancement , In image restoration , Degradation is modeled . It can （ For the most part ） Eliminate the effects of degradation .

1、 Image degradation type

Image degradation

         The goal of image restoration is to restore the degraded image to its original form .

2、 Deconvolution and degenerate model

         Observed images can usually be modeled as ： Where integral is convolution , Is the point spread function of the imaging system , It's additive noise .

         under these circumstances , The purpose of image restoration is to recover from observed degraded images Estimate the original image .

         The model degenerates to linear 、 Shift invariants 、 filter Convolution of .

         Example ： For out of focus blur , take Modeled as Gauss

         , Is the impulse response or point spread function of the imaging system

3、 Information loss and noise

 4、 Formula definition

        – Image before degradation ,“ Real images ”

         – Degraded image ,“ Observed images ”

         –  Degradation filter

         – according to Calculated The estimate of

         – Additive noise

Two 、inverse filter

         Start by generating the model , Temporary neglect , Then get The estimate of

         Use the inverse filter to recover

 1、 One dimensional vector description

2、 To blur （ deconvolution ）

         Blur the image with Gaussian point spread function

          Use the inverse filter to recover , among It's Gauss FT.

 3、 Noise amplification problem

          High spatial frequency sine wave

3、 ... and 、Wiener filter

1、 Wiener filtering

           Use Wiener filter to recover

2、 Use Wiener filter to recover

 3、 Formula derivation

 4、 Motion blur

         Suppose there is only ambiguity in the horizontal direction , for example ： Camera pan when image is acquired

1. Calculate the of blurred image FT
2. take FT multiply Wiener filter F(u,v) = W(u,v) G(u,v)
3. Computational inverse FT

 5、 application ： Read the license plate

        computational procedure

        1. Rotated image , Make the blur horizontal
        2. Estimate the fuzzy length
        3. Build a bar graph that models convolution
        4. Calculate and apply Wiener filter
        5. Optimize K value

Four 、 Maximum posteriori （MAP） It is estimated that

         Maximum posterior estimate (Maximum-a-Posteriori (MAP) Estimation)

1、 Generate models

          Those who have n Pixel image , Write this process as , among and yes Dimension vector ,A yes matrix .

2、 Inverse problem

         Estimate by optimizing the cost function ：

 3、 Example ： Super resolution

         Suppose there are multiple images of the same scene , Every image is shifted in space ……

 4、 Generate models

          Estimate a super-resolution image that minimizes the error between the predicted image and the observed image .

         Put an image   The generation model of is written as , among Combined with positioning 、 Lighting and down sampling .

 5、 Maximum posterior estimate

6、 Super resolution example 1

         The Mars Lander provides 25 Zhang JPEG Images images come from different scans of the rotating camera

7、 Super resolution example 2

  5、 ... and 、Blind deblurring

1、 summary

          up to now , We have a premise , It is assumed that we know the generation model , for example

          namely h(x,y) It is known. , So given the observed image g(x,y), It can be estimated that （ recovery ） original image f(x,y)

         Consider whether only observed images g(x,y) It is known. . This is the problem of blind estimation .

         Estimate by optimizing the cost function f(x,y) and h(x,y)：

 2、 Example