We present an intelligent programmable computational meta-imager that tailors its sequence of coherent scene illuminations not only to a specific information-extraction task (e.g., object recognition) but also adapts to different types and levels of noise. We systematically study how the learned illumination patterns depend on the noise, and we discover that trends in intensity and overlap of the learned illumination patterns can be understood intuitively. We conduct our analysis based on an analytical coupled-dipole forward model of a microwave dynamic metasurface antenna (DMA); we formulate a differentiable end-to-end information-flow pipeline comprising the programmable physical measurement process including noise as well as the subsequent digital processing layers. This pipeline allows us to jointly inverse-design the programmable physical weights (DMA configurations that determine the coherent scene illuminations) and the trainable digital weights. Our noise-adaptive intelligent meta-imager outperforms the conventional use of pseudo-random illumination patterns most clearly under conditions that make the extraction of sufficient task-relevant information challenging: latency constraints (limiting the number of allowed measurements) and strong noise. Programmable microwave meta-imagers in indoor surveillance and earth observation will be confronted with these conditions.