I am not a mathematician so my question might appear lame to you all; anyways, here I go.
I work with images and here in this problem, I would like to blow up the resolution of the image. Let's say we got a $5\times 5$ pixel matrix with some values which represent a small portion of the image. If $1\times 1$ pixel is a representation of $1$ metre by $1$ metre area on the ground my idea is to combine the neighbouring pixels say a bunch of $5$ pixels and blow up the matrix to a $50\times 50$. By doing so, I gotta resolution enhancement of $10$ folds.
At the moment I am trying out $\text{sinc}(x)$ function but I am unable to arrive at the analytical formulation. By now I hope you all gotta hold of my problem. The idea is to use the existing values in the $5\times 5$ matrix and fit some sort of a continuous surface which will recreate the intermediate values thereby expanding the matrix to a $50\times 50$ one.
I have attached some images for your reference. Focus on the distribution of the points and no matter what the curve still fill the gaps. I want to achieve this in $2$-Dimension.
Eagerly waiting for your suggestions guys...
