Copyright 2015 by D.G. Long at Brigham Young University.  All rights reserved.
Source code may be used for non-commerical purposes so long as paper is cited.

Matlab source that demonstrates 2d reconstruction from variable aperture
irregular sampling described in

D.G. Long and R. Franz, Bandlimited Signal Reconstruction from Irregular 
  Samples with Variable Apertures, IEEE Trans. Geosci. Remote Sensing, 2015.

**************************************************************

Key files:

demo_irregrecon2d.m : demonstrates 2d sampling and reconstruction w/o aperture
demo_irregrecon2dAp.m : demonstrates 2d sampling and reconstruction w/aperture
irregrecon2d.m : 2d reconstruction w/o aperature
irregrecon2dAp.m : 2d reconstruction w/aperature
test_sampling2d.m : test 2d sampling
checkrankD.m : generates and tests rank of D1 matrix w/o aperture
checkrankD_Ap.m : generates and test rank of Dv matrix (D1 w/aperture)

Support files:

Dm.m : compute 1d M-order Dirichlet function
Dm2d.m : compute 2d M1,M2-order Dirichlet function
ApDm2d.m : compute 2d aperture-filtered M1,M2-order Dirichlet function
plotlocs.m : plot 2d sample locations
myfigure.m : matlab routine to provide functionality similar to figure.m
randsample1d.m : 1d sampling routine
randsample2d.m : 2d sampling routine
README.txt : this file

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Matlab notes:

Two dimensional arrays in Matlab can sometimes be confusing so the following
simple examples and notes are provided.  Note that Matlab images by default 
have their origin at the upper left corner, which matches the Matlab matrix 
convention used below.

By convention in this Matlab implemenation, M1 and N1 are associated with 
the column (x or I) axis, while M2 and N2 are associated with the 
row (y or J) axis. An N1xN2 array A is thus dimensioned A=zeros([N2,N1]).
Note that Matlab uses column-first indexing for one-dimensional indexing
of two-dimensional arrays. Thus,

>> A=[1 4; 2 5; 3 6] % semi-colons separate rows on entry

A =             % {x,cols ->  y,rows \/}
     1     4
     2     5
     3     6

>> [N2,N1]=size(A)

N2 =
     3

N1 =
     2

>> A(3,2) % A(row=3,col=2)

ans =
    6

>> A(:)   % produces a column vector

ans =
     1
     2
     3
     4
     5
     6

>> x=floor((A-1)/N2)+1  % x (col) [N1] cordinate location is

x =
     1     2
     1     2
     1     2

>> y=mod(A-1,N2)+1  % y (row) [N2] coordinate location is

y =
     1     1
     2     2
     3     3

>> [y,x]=ind2sub([N2,N1],A) % equivalent to two previous statements

y =
     1     1
     2     2
     3     3

x =
     1     2
     1     2
     1     2

>> y(:)   % produces a column vector

ans =
     1
     2
     3
     1
     2
     3

>> x(:)   % produces a column vector

ans =
     1
     1
     1
     2
     2
     2

>> A=sub2ind([N2,N1],y,x)

A =
     1     4
     2     5
     3     6

>> A=y+(x-1)*N2  % equvalent to previous statement

A =
     1     4
     2     5
     3     6

> [y,x]=ind2sub([N2,N1],A(:))    % produces column vectors

y =
     1
     2
     3
     1
     2
     3

x =
     1
     1
     1
     2
     2
     2

>> sub2ind([N2,N1],y(:),x(:))  % produces column vectors

ans =
     1
     2
     3
     4
     5
     6

>> cols=[1 2]; rows=[1 2 3];   % for cubic lattice locations
>> [x,y]=meshgrid(cols,rows)

x =
     1     2
     1     2
     1     2

y =
     1     1
     2     2
     3     3

>> x=repmat(cols,length(rows),1)  % equiv to previous line 
>> y=repmat(rows',1,length(cols)) 

x =
     1     2
     1     2
     1     2

y =
     1     1
     2     2
     3     3