Image Processing Toolbox

Deblurring Model

A blurred or degraded image can be approximately described by this equation g = Hf + n, where:

• g = The blurred image

  H = The distortion operator, also called the point-spread function (PSF). This function, when convolved with the image, creates the distortion

  f = The original true image

  n = Additive noise, introduced during image acquisition, that corrupts the image

Note    The image f really doesn't exist. This image represents what you would have if you had perfect image acquisition conditions.

The Importance of the PSF

Based on this model, the fundamental task of deblurring is to deconvolve the blurred image with the PSF that exactly describes the distortion.

Note    The quality of the deblurred image is mainly determined by knowledge of the PSF.

To illustrate, this example takes a clear image and deliberately blurs it by convolving it with a PSF. The example uses the fspecial function to create a PSF that simulates a motion blur, specifying the length of the blur in pixels, (LEN=31), and the angle of the blur in degrees (THETA=11). Once the PSF is created, the example uses the imfilter function to convolve the PSF with the original image, I, to create the blurred image, Blurred. (To see how deblurring is the reverse of this process, using the same images, see Deblurring with the Wiener Filter.)

• I = imread('flowers.tif');
  I = I(10+[1:256],222+[1:256],:); % crop the image
  figure;imshow(I);title('Original Image');
  
  LEN = 31;
  THETA = 11;
  PSF = fspecial('motion',LEN,THETA);
  Blurred = imfilter(I,PSF,'circular','conv');
  figure; imshow(Blurred);title('Blurred Image');
  
  
  

Understanding Deblurring

Using the Deblurring Functions