Is there a two-dimensional sinc interpolation software?

Hello everyone. I have found this package of software. I am interested in doing a two-dimensonal sinc interpolation as defined in the diapositives 15 to 18 of this presentation. Unfortunately. I haven't found anything.

Can anybody point me to some code that might work?

Best regards.

Jaime.

Answer 1

[Star Strider]

One-dimensional sinc interplation is described in Ideal Bandlimited Interpolation. It may be possible to adapt it to a 2D problem.

.

[Matt J]

Yes, it is possible, but this is only valid for plaid upsampling, not arbitrary interpolation.

Image=double(imread('cameraman.tif'));
M=length(Image);

t=1:M;
dt=0.2;
ts = -M:dt:2*M;
[Ts,T] = ndgrid(ts,t);
A=sinc(Ts - T);
A([1:M/dt,end+1-M/dt:end],:)=[];

ImageInterpolated = A*Image*A.';

whos Image ImageInterpolated

  Name                      Size                 Bytes  Class     Attributes

  Image                   256x256               524288  double              
  ImageInterpolated      1281x1281            13127688  double              

imshow(ImageInterpolated,[])

[Jaime De La Mota Sanchis]

That is great, since I have a grid of size 19*13 with values of temperature and I want to find an equation using this sinc interpolation to have a function to describe said field. Is there a way to adapt this code so that instead of an image, a matrix is introduced and the resulting expressin can be read?

Answer 2

[Matt J]

Since interpolation is commonly approximated by cubic spline interpolation, which you have an option for in interp2.

Vq = interp2(X,Y,V,Xq,Yq,'spline');

[Jaime De La Mota Sanchis]

Thanks for the answer. Is there a way to find the equation used to build said interpolation?

Answer 3

[Nikeet Pandit]

We know that Fourier is a seperable transform... so if we want to do a Fourier 2D transform its equivalent to doing 1D transform on rows and then columns. I assume then this property holds for sinc interpolation... So I adapted the 1D example for sinc interpolation they provide on the sinc(x) documentation ... and then I applied the interpolation to the rows and then interpolation to the columns and it seemed to work