We propose a machine learning approach for image regression from sparse experimental measurements. We show the application of the proposed method on film cooling studies in propulsion system development, aiming to reduce the need for extensive physical testing. Our method employs a lightweight feed-forward neural network with positional encoding to generate images conditioned by input parameters. Validated on real and synthetic data, it achieves high image similarity (RMSE < 8 %, SSIM > 93 %) while maintaining accuracy with a 30 \% reduction of measurements. We further propose a knowledge-informed extension for local adaptability of the generated images. This approach significantly reduces required tests while preserving high-quality data, enabling efficient optimization of coolant injector configurations with applications beyond aerospace.