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Inpaint over missing data in 1-D, 2-D, 3-D,... N-D arrays

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Inpaint over missing data in 1-D, 2-D, 3-D,... N-D arrays

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23 Jun 2010 (Updated )

Y = INPAINTN(X) computes the missing data in the N-D array X.

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Description

Y = INPAINTN(X) replaces the missing data in X by extra/interpolating the non-missing elements. The non finite values (NaN or Inf) in X are considered as missing data. X can be any N-D array.

Type "help inpaintn" in the Matlab command windows for several examples.

INPAINTN (no input/output argument) runs a 3-D example.
 
Important note:
----------------
INPAINTN uses an iterative process that converges toward the solution. Y = INPAINTN(X,N) uses N iterations. By default, N = 100. If you estimate that INPAINTN did not totally converge, then increase N: Y = INPAINTN(X,1000);

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When using this algorithm, please refer to these 2 papers:

1) Garcia D. Robust smoothing of gridded data in one and higher dimensions with missing values.
Comput Statist Data Anal, 2010;54:1167-1178
http://www.biomecardio.com/pageshtm/publi/csda10.pdf

2) Wang G, Garcia D et al. A three- dimensional gap filling method for large geophysical datasets: Application to global satellite soil moisture observations.
Environ Modell Softw, 2012;30:139-142.
http://www.biomecardio.com/pageshtm/publi/envirmodellsoftw12.pdf.pdf
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Example:
--------
%% ---- 2-D data ---- %%
n = 256;
y0 = peaks(n);
y = y0;
I = randperm(n^2);
y(I(1:n^2*0.5)) = NaN; % lose 1/2 of data
y(40:90,140:190) = NaN; % create a hole
z = inpaintn(y,200); % inpaint data
subplot(2,2,1:2), imagesc(y), axis equal off
title('Corrupt data')
subplot(223), imagesc(z), axis equal off
title('Recovered data ...')
subplot(224), imagesc(y0), axis equal off
title('... compared with original data')

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http://www.biomecardio.com
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Acknowledgements

Inpaint Nans, Inpainting Nan Elements In 3 D, and Dct And Dst (+ Inverse) In Arbitrary Dimension inspired this file.

This file inspired Pi Vsuite.

MATLAB release MATLAB 7.10 (R2010a)
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Comments and Ratings (13)
04 Feb 2014 Keith

Great work, been running well for me until I ran into an issue today. I received the error code:

??? Subscript indices must either be real positive integers or logicals.

Error in ==> inpaintn>InitialGuess at 179
z(~I) = y(L(~I));

Error in ==> inpaintn at 142
[y,s0] = InitialGuess(x,isfinite(x));

Error in ==> test at 32
betas_paint2(:,k) = inpaintn(betas_paint(:,k));

Was trying to run inpaintn through an external loop feeding it vectors. It made it through the first 8 then gave me an error. Any help is appreciated.

31 Jan 2014 Ryan Muir

This is a great program! It is easy to use, and is really impressively fast.

I was using it for 3D and 4D interpolation of rather large problems, and was taking hours per image to process. I found that I could offload much of the problem to the GPUs, and get an order of magnitude more speed with a couple of lines of extra code! It's a bit sloppy, but putting y = gpuArray(y) near the beginning of the cdtn() and icdtn() functions bought me this performance enhancement. There are likely more efficient and elegant ways of sending it to the GPU, though this way worked great in a pinch. Small problems (including the example problem) run a bit slower with this modification, so this really is for large problems only.

09 Aug 2013 Jeff

I'm incorrect. Apologies.

Although I had downloaded Damien's new version of inpaintn, I had earlier used the older version (that I had neglected to delete), in a folder that put it ahead of the new version.

08 Aug 2013 Jeff

The call to test4DCTNANDIDCTN can be eliminated because the functions dctn and idctn are now included in the inpaintn.m file.

Otherwise, works well. Results in my application compare reasonably with John D'Errico's inpaint_nans3, and is faster.

31 Jul 2013 Marc Crapeau

Very good submission. I was working on my own version of this problem when a google research send me here and save me several hours of work. Thanks!

10 May 2013 Shrinivas

I am getting error
??? Error: File: inpaintn.m Line: 176 Column: 7
Expression or statement is incorrect--possibly unbalanced (, {, or [.

09 May 2013 Scott Richardson

Hi, thank you for sharing this.

Do you happen to have onion.png, and wind.mat to try the other examples?

30 Oct 2012 yo

hey everyone, the looks great, but unfotunately i've been getting the following error:

Error in ==> inpaintn at
140
y =
RF*idctn(Gamma.*dctn(W.*(x-y)+y))
+ (1-RF)*y;

since i don't feel capable enpugh changing the code on my own, can someone tell me what went wrong?

Thanks alot,

yoav

01 Mar 2012 Kyle

Very useful script. I will never use matlab extrapolation routines ever again.

01 Mar 2012 Kyle  
08 Nov 2011 tudor dima

Great work, extremely useful, it works out of the box.
Thanks a lot for posting it!

Would there be a simple way to restrict calculations inside a "gating mask"?

12 Oct 2010 Bohuslav Ruzek

I had to interpolate missing 3D geophysical data in order to enable standard filtration process. Inpaint code worked very well for this, the results look pretty well. Using inpaint is easy.
I recommend using this script also for other interested users.

29 Jul 2010 Leonardo

Very useful, works nicely. The only issue is that a couple of additional functions (dctn and idctn) have to be downloaded from another site for this to work

Updates
24 Jun 2010

Image toolbox is no longer required.

25 Jun 2010

1) there was a mistake in the 4-D example
2) an initial guess can be now given as an input

08 May 2013

The functions DCTN and IDCTN are now included in INPAITN

11 Nov 2013

Update of the help text

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