Talk:Richardson–Lucy deconvolution

Untitled

The paragraph says "In the presence of noise, pixels in the observed image can be represented in terms of the point spread function and the latent image as..." but I can't see the noise in the equation. Does it lack an aditive term (+ epsilon) that takes into account Photon noise?

I think the equations here are correct: the noise is modelled by having $u_{i}$ as a random variable with a Poisson distribution. This becomes clear in the derivation of the iteration, something which I plan to add to the article. Chrisjohnson 00:18, 8 April 2007 (UTC)

Original paper reference

Should not the reference to the original paper in this article be to the "Astronomical Journal", not just to the "AJ"? (I've seen confusions of this sort before - example: "APJ" or "ApJ", when "Astrophysical Journal" - rather than "Applications Journal" - was meant.) Hair Commodore 21:44, 18 December 2006 (UTC)

Googling reveals that the Astronomical Journal refers to itself as AJ or Astron. J. I've put the latter into the article. Chrisjohnson 00:18, 8 April 2007 (UTC)

Layman description

I study computer sciences, and was assigned a paper about this algorithm. I used MATLAB's implementation to demonstrate it in action, but my teachers are now requiring a layman's explanation of the algorithm. Does anybody know where I can find such a thing, or if it's even possible to explain it without advanced math? Mfuhlendorf 8 November 2007 Thanks.

I think you can get the article from Journal of the Optical Society of America (Vol. 62, No. 1, 1972) if your school has subscribed this journal. Besides I think only discussions on the topic itself should be put in this page. Zhuoxi huo (talk) 10:10, 1 July 2010 (UTC)

example/ explinations

so I was thinking this could do with maybe a bit more explanation for folks that may have trouble grasping the index based description of this algorithm. If no one complains I might add the following to the main article in a few days time...

A more accessible description using element wise multiplication and division with the convolution operator is

$u_{t+1}=u_{t}\cdot \left({\frac {d}{u_{t}\otimes p}}\otimes p\right)$

Where $u_{t}$ is the $t$^th estimate of the latent image $u$; $d$ the observed blurred image and $p$ the blur kernel/PSF. This formulation, while still true for the 1D case, also illustrates how this algorithm works in 2D as well.

MatLab has a function that will perform devolution but for educational purposes this may be also handy

function latent_est = RL_deconvolution(observed, kernel, max_iterations)
    % to utilise the conv2 function we must make sure the inputs are double
    observed = double(observed);
    kernel = double(kernel);
    %start estimate uniform 50% grey - this can be picked as you like
    latent_est = 0.5*ones(size(observed));
    % iterate towards ML estimate for the latent image
    for i= 1:max_iterations
        est_convolved = conv2(latent_est,kernel,'same');
        relitive_blur = observed./est_convolved;
        errror_est = conv2(relitive_blur,kernel,'same'); 
        latent_est = latent_est.*errror_est;
        % draw output
        subplot(1,2,1)
        imagesc(observed); colormap('gray');
        title('blured original')
        subplot(1,2,2)
        imagesc(latent_est);colormap('gray');
        title(['iteration #' int2str(i)])
        drawnow;
    end

In the article page, the second point spread function is flipped. But here, it is not. Could you explain why ? RegardsAlexyangfox (talk) 03:30, 4 August 2014 (UTC)

tried to make it more intuitive, but failed.

I am sort of a layman. I tried to make it more intuitive,but failed. It would be very nice if someone could point out where I am wrong.

here is my reasoning:

$u_{j}^{(t+1)}=u_{j}^{(t)}\sum _{i}{\frac {d_{i}}{c_{i}}}p_{ij}$

where

$c_{i}=\sum _{j}p_{ij}u_{j}^{(t)}.$

if the first equation above converges to $u_{j}$ ,I think all j elements in $\sum _{i}{\frac {d_{i}}{c_{i}}}p_{ij}$ would approach one. It is very easy to check that all i elements in ${\frac {d_{i}}{c_{i}}}$ will approach 1. And this makes me so confused. The PSF will not be just a single point,this means it will make the j elements in $\sum _{i}{\frac {d_{i}}{c_{i}}}p_{ij}$ other than one.

Where am I wrong? Regards. Alexyangfox (talk) 03:06, 3 August 2014 (UTC)

I found out why! Because the sum of the elements in a PSF is one .Alexyangfox (talk) 03:24, 4 August 2014 (UTC)

"flipped"?

Is "flipped" some formal matrix operation that I should know about? Sounds more like something for pancakes.

2600:1700:C280:3FD0:8058:E8A0:B837:8E95 (talk) 16:39, 6 July 2021 (UTC)

Formally, it's the adjoint from:

$\langle A*B,C\rangle =\langle A,B^{*}*C\rangle$

where $B^{*}(x,y)=B(-x,-y)$. So the order of rows and columns of a matrix get "flipped." Maybe it can be clearer in the text. Maqifrnswa (talk) 21:22, 26 February 2024 (UTC)

Derivation

https://en.wikipedia.org/w/index.php?title=Richardson%E2%80%93Lucy_deconvolution&diff=next&oldid=1094544109

Could we maybe be more constructive on my this derivation is getting nuked repeatedly? — Preceding unsigned comment added by 86.156.0.78 (talk) 21:39, 7 October 2022 (UTC)