A smooth and sharp image interpolation you probably haven't heard of

Neat aside, k = 1/x^∞ seems to be equivalent to nearest neighbor. (please excuse the abuse of notation)

Really at any size I tried, I found the "upscale" to look blurry / low quality.

Am I an outlier here?

    k(x) = 1/x
    
        y_i * k(x - x_i) + y_i+1 * k(x_i+1 - x)
    F = --------------------------------------- =
             k(x - x_i) + k(x_i+1 - x)
    
      y_i / (x - x_i) + y_i+1 / (x_i+1 - x)
    = --------------------------------------- =
           1 / (x - x_i) + 1 / (x_i+1 - x)
    
      y_i * (x_i+1 - x) / A + y_i+1 * (x - x_i) / A
    = ---------------------------------------------
           (x_i+1 - x) / A + (x - x_i) / A
    
    where A = (x - x_i) * (x_i+1 - x)
    scaling to x_i+1 - x_i = 1, and using a = (x - x_i)
    
    F = (1 - a) * y_i + a * y_i+1

SuperXBR is in the family of Edge-Directed interpolation algorithms, so diagonal or curved lines will properly maintain their shape when upscaled, and not produce "staircase" artifacts that you see with other classical interpolation. It does not improve the sharpness though, images will still look blurry after being upscaled, just like when you perform bilinear upscaling.

But if you are doing any kind of non-realtime image upscaling today, you'd want to use the modern AI algorithms, such as Waifu2x or ESRGAN.

It's like nearest neighbor interpolation but with less artifacting when the zoom is not an integer. The middle of each source pixel becomes a solid color block, and then bilinear filtering is applied to the single-pixel-wide seams between each block.

It's equivalent to doing a nearest neighbor upscale to floor(scale), then finishing with bilinear.