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In keras it is possible to use UpSampling2D layer to up-sample an image. You can use Bilinear Interpolation.

Given an image ${h\times w}$ it is possible to increase its size in ${h*k\times w*l}$, where $k$ and $l$ are factors greater than or equal to $1$.

I understand the Bilinear Interpolation formula applied to $4$ neighbouring pixels (${2\times 2}$ sub-matrix). But I just can't figure out how to apply it to perform up-sampling. What is the actual algorithm being implemented? How is Bilinear Interpolation mathematically defined for up-sampling 2D images?

Nowhere have I found the real algorithm, no one explains how to construct the new matrix correctly and consistently. It is always explained in an incomprehensible way, please help me.

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