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Deblur image using Lucy-Richardson method



J = deconvlucy(I,psf) restores image I that was degraded by convolution with a point-spread function (PSF), psf, and possibly by additive noise. The algorithm is based on maximizing the likelihood that the resulting image J is an instance of the original image I under Poisson statistics.

To improve the restoration, deconvlucy supports several optional parameters, described below. Use [] as a placeholder if you do not specify an intermediate parameter.


J = deconvlucy(I,psf,iter) specifies the number of iterations, iter.

J = deconvlucy(I,psf,iter,dampar) controls noise amplification by suppressing iterations for pixels that deviate a small amount compared to the noise, specified by the damping threshold dampar. By default, no damping occurs.

J = deconvlucy(I,psf,iter,dampar,weight) specifies which pixels in the input image I are considered in the restoration. The value of an element in the weight array determines how much the pixel at the corresponding position in the input image is considered. For example, to exclude a pixel from consideration, assign it a value of 0 in the weight array. You can adjust the weight value assigned to each pixel according to the amount of flat-field correction.

J = deconvlucy(I,psf,iter,dampar,weight,readout) specifies the additive noise (such as background or foreground noise) and variance of the read-out camera noise, readout.

J = deconvlucy(I,psf,iter,dampar,weight,readout,subsample) uses subsampling when the PSF is given on a grid that is subsample times finer than the image.


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Read and display a pristine image that does not have blur or noise. This example optionally crops the image to a size of 256-by-256 with the top-left (x,y) coordinate at (2,50).

I = imread('board.tif');
I = imcrop(I,[2 50 255 255]);
title('Original Image')

Figure contains an axes. The axes with title Original Image contains an object of type image.

Create a PSF that represents a Gaussian blur with standard deviation 5 and filter of size 5-by-5.

PSF = fspecial('gaussian',5,5);

Simulate blur in the image.

blurred = imfilter(I,PSF,'symmetric','conv');

Add simulated zero-mean Gaussian noise.

V = 0.002;
blurred_noisy = imnoise(blurred,'gaussian',0,V);
title('Blurred and Noisy Image')

Figure contains an axes. The axes with title Blurred and Noisy Image contains an object of type image.

Use deconvlucy to restore the blurred and noisy image. Specify the PSF used to create the blur and decrease the number of iterations to 5.

luc1 = deconvlucy(blurred_noisy,PSF,5);
title('Restored Image')

Figure contains an axes. The axes with title Restored Image contains an object of type image.

Create a sample image and blur it.

I = checkerboard(8);
PSF = fspecial('gaussian',7,10);
V = .0001;
BlurredNoisy = imnoise(imfilter(I,PSF),'gaussian',0,V);

Create a weight array and call deconvlucy using several optional parameters.

WT = zeros(size(I));
WT(5:end-4,5:end-4) = 1;
J1 = deconvlucy(BlurredNoisy,PSF);
J2 = deconvlucy(BlurredNoisy,PSF,20,sqrt(V));
J3 = deconvlucy(BlurredNoisy,PSF,20,sqrt(V),WT);

Display the results.

title('A = Blurred and Noisy');

Figure contains 4 axes. Axes 1 with title A = Blurred and Noisy contains an object of type image. Axes 2 with title deconvlucy(A,PSF) contains an object of type image. Axes 3 with title deconvlucy(A,PSF,NI,DP) contains an object of type image. Axes 4 with title deconvlucy(A,PSF,NI,DP,WT) contains an object of type image.

Input Arguments

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Blurry image, specified as a numeric array of any dimension. You can also specify the image as a cell array to enable interrupted iterations. For more information, see Tips.

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

PSF, specified as a numeric array.

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

Number of iterations, specified as a positive integer.

Data Types: double

Threshold for damping, specified as a numeric scalar. Damping occurs for pixels whose deviation between iterations is less than the threshold. dampar has the same data type as I.

Weight value of each pixel, specified as a numeric array with values in the range [0, 1]. weight has the same size as the input image, I. By default, all elements in weight have the value 1, so all pixels are considered equally in the restoration.

Data Types: double

Noise, specified as a numeric scalar or numeric array. The value of readout corresponds to the additive noise (such as noise from the foreground and background) and the variance of the read-out camera noise. readout has the same data type as I.

Subsampling, specified as a positive scalar.

Data Types: double

Output Arguments

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Deblurred image, returned as a numeric array or a 1-by-4 cell array. J (or J{1} when J is a cell array) has the same data type as I. For more information about returning J as a cell array for interrupted iterations, see Tips.


  • You can use deconvlucy to perform a deconvolution that starts where a previous deconvolution stopped. To use this feature, pass the input image I as a cell array, {I}. When you do, the deconvlucy function returns the output image J as a cell array, which you can then pass as the input array into the next deconvlucy call. The output cell array J contains four elements:

    J{1} contains I, the original image.

    J{2} contains the result of the last iteration.

    J{3} contains the result of the next-to-last iteration.

    J{4} is an array generated by the iterative algorithm.

  • 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 deconvlucy.

  • deconvlucy converts the PSF to double without normalization.

  • deconvlucy may return values in the output image that are beyond the range of the input image.


[1] D.S.C. Biggs and M. Andrews, Acceleration of iterative image restoration algorithms, Applied Optics, Vol. 36, No. 8, 1997.

[2] R.J. Hanisch, R.L. White, and R.L. Gilliland, Deconvolutions of Hubble Space Telescope Images and Spectra, Deconvolution of Images and Spectra, Ed. P.A. Jansson, 2nd ed., Academic Press, CA, 1997.

Introduced before R2006a