Optimizing noise-based pixelated shader.

I currently have a working shader that generates noise-based textures and posterizes the uv lookups on each texel (multiplying by arbitrary value + rounding) to get a pixelated look.

I guess the optimal way to go would be generating a texture on the fly on the minimal needed resolution and then filtering that result with a nearest filter at full resolution, instead of computing the whole pixel shader for each texel as I´m doing right now. Would that be possible to do in a single shader? (I´m using Unity Indie) Thanks in advance!