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# Image Processing Toolbox

## Deblurring Images Using a Wiener Filter

Wiener deconvolution can be useful when the point-spread function and noise level are known or can be estimated.

### Contents

```I = im2double(imread('cameraman.tif'));
imshow(I);
title('Original Image (courtesy of MIT)');
```

### Simulate a Motion Blur

Simulate a blurred image that you might get from camera motion. Create a point-spread function, PSF, corresponding to the linear motion across 31 pixels (LEN=31), at an angle of 11 degrees (THETA=11). To simulate the blur, convolve the filter with the image using imfilter.

```LEN = 21;
THETA = 11;
PSF = fspecial('motion', LEN, THETA);
blurred = imfilter(I, PSF, 'conv', 'circular');
imshow(blurred);
title('Blurred Image');
```

### Restore the Blurred Image

The simplest syntax for deconvwnr is deconvwnr(A, PSF, NSR), where A is the blurred image, PSF is the point-spread function, and NSR is the noise-power-to-signal-power ratio. The blurred image formed in Step 2 has no noise, so we'll use 0 for NSR.

```wnr1 = deconvwnr(blurred, PSF, 0);
imshow(wnr1);
title('Restored Image');
```

### Simulate Blur and Noise

```noise_mean = 0;
noise_var = 0.0001;
blurred_noisy = imnoise(blurred, 'gaussian', ...
noise_mean, noise_var);
imshow(blurred_noisy)
title('Simulate Blur and Noise')
```

### Restore the Blurred and Noisy Image: First Attempt

In our first restoration attempt, we'll tell deconvwnr that there is no noise (NSR = 0). When NSR = 0, the Wiener restoration filter is equivalent to an ideal inverse filter. The ideal inverse filter can be extremely sensitive to noise in the input image, as the next image shows:

```wnr2 = deconvwnr(blurred_noisy, PSF, 0);
imshow(wnr2)
title('Restoration of Blurred, Noisy Image Using NSR = 0')
```

The noise was amplified by the inverse filter to such a degree that only the barest hint of the man's shape is visible.

### Restore the Blurred and Noisy Image: Second Attempt

In our second attempt we supply an estimate of the noise-power-to-signal-power ratio.

```signal_var = var(I(:));
wnr3 = deconvwnr(blurred_noisy, PSF, noise_var / signal_var);
imshow(wnr3)
title('Restoration of Blurred, Noisy Image Using Estimated NSR');
```

### Simulate Blur and 8-Bit Quantization Noise

Even a visually imperceptible amount of noise can affect the result. Let's try keeping the input image in uint8 representation instead of converting it to double.

```I = imread('cameraman.tif');
class(I)
```
```ans =

uint8

```

If you pass a uint8 image to imfilter, it will quantize the output in order to return another uint8 image.

```blurred_quantized = imfilter(I, PSF, 'conv', 'circular');
class(blurred_quantized)
```
```ans =

uint8

```

### Restore the Blurred, Quantized Image: First Attempt

Again, we'll try first telling deconvwnr that there is no noise.

```wnr4 = deconvwnr(blurred_quantized, PSF, 0);
imshow(wnr4)
title('Restoration of blurred, quantized image using NSR = 0');
```

### Restore the Blurred, Quantized Image: Second Attempt

Next, we supply an NSR estimate to deconvwnr.

```uniform_quantization_var = (1/256)^2 / 12;
signal_var = var(im2double(I(:)));
wnr5 = deconvwnr(blurred_quantized, PSF, ...
uniform_quantization_var / signal_var);
imshow(wnr5)
title('Restoration of Blurred, Quantized Image Using Computed NSR');
```