Talk:Richardson–Lucy deconvolution

message: 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)
thread_title: Untitled

message: 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)
replies: text: 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)
thread_title:  Original paper reference 

message: 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)
thread_title:  Layman description 

message: 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 tth 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)
thread_title:  example/ explinations 

message: 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)
replies: text:  I found out why! Because the sum of the elements in a PSF is one .Alexyangfox (talk) 03:24, 4 August 2014 (UTC)
thread_title:  tried to make it more intuitive, but failed. 

message: 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)
thread_title:  Derivation