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deconvwnr

Deblur image using Wiener filter

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Syntax

J = deconvwnr(I,psf,nsr)
J = deconvwnr(I,psf,ncorr,icorr)
J = deconvwnr(I,psf)

Description

J = deconvwnr(I,psf,nsr) deconvolves image I using the Wiener filter algorithm, returning deblurred image J. psf is the point-spread function (PSF) with which I was convolved. nsr is the noise-to-signal power ratio of the additive noise. The algorithm is optimal in a sense of least mean square error between the estimated and the true images.

example

J = deconvwnr(I,psf,ncorr,icorr) deconvolves image I, where ncorr is the autocorrelation function of the noise and icorr is the autocorrelation function of the original image.

J = deconvwnr(I,psf) deconvolves image I using the Wiener filter algorithm with no estimated noise. In the absence of noise, a Wiener filter is equivalent to an ideal inverse filter.

Examples

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Open Live Script

Read image into the workspace and display it.

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

Figure contains an axes object. The hidden axes object with title Original Image (courtesy of MIT) contains an object of type image.

Simulate a motion blur.

LEN = 21;
THETA = 11;
PSF = fspecial('motion', LEN, THETA);
blurred = imfilter(I, PSF, 'conv', 'circular');
figure, imshow(blurred)

Figure contains an axes object. The hidden axes object contains an object of type image.

Simulate additive noise.

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

Figure contains an axes object. The hidden axes object with title Simulate Blur and Noise contains an object of type image.

Try restoration assuming no noise.

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

Figure contains an axes object. The hidden axes object with title Restoration of Blurred, Noisy Image Using NSR = 0 contains an object of type image.

Try restoration using a better estimate of the noise-to-signal-power ratio.

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

Figure contains an axes object. The hidden axes object with title Restoration of Blurred, Noisy Image Using Estimated NSR contains an object of type image.

Input Arguments

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Blurry image, specified as a numeric array of any dimension.

Data Types: single | double | int16 | uint8 | uint16

Point-spread function, specified as a numeric array.

Data Types: double

Noise-to-signal ratio, specified as a nonnegative scalar or numeric array of the same size as the image, I. If nsr is an array, then it represents the spectral domain. Specifying 0 for the nsr is equivalent to creating an ideal inverse filter.

Data Types: double

Autocorrelation function of the noise, specified as a numeric array of any size or dimension, not exceeding the original image.

  • If the dimensionality of ncorr matches the dimensionality of the image I, then the values correspond to the autocorrelation within each dimension.

  • If ncorr is a vector and psf is also a vector, then the values in ncorr represent the autocorrelation function in the first dimension.

  • If ncorr is a vector and psf is an array, then the 1-D autocorrelation function is extrapolated by symmetry to all non-singleton dimensions of psf.

  • If ncorr is a scalar, then the value represents the power of the noise.

Data Types: double

Autocorrelation function of the image, specified as a numeric array of any size or dimension, not exceeding the original image.

  • If the dimensionality of icorr matches the dimensionality of the image I, then the values correspond to the autocorrelation within each dimension.

  • If icorr is a vector and psf is also a vector, then the values in icorr represent the autocorrelation function in the first dimension.

  • If icorr is a vector and psf is an array, then the 1-D autocorrelation function is extrapolated by symmetry to all non-singleton dimensions of psf.

  • If icorr is a scalar, then the value represents the power of the image.

Data Types: double

Output Arguments

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Deblurred image, returned as a numeric array. J has the same data type as I.

Tips

  • The output image J could exhibit ringing introduced by the discrete Fourier transform used in the algorithm. To reduce the ringing, use I = edgetaper(I,psf) before calling deconvwnr.

References

[1] Gonzalez, R. C., and R. E. Woods. Digital Image Processing. Addison-Wesley Publishing Company, Inc., 1992.

Version History

Introduced before R2006a

See Also

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