Extremely high data rates expected in next-generation radio interferometers necessitate a fast and robust way to process measurements in a big data context. Dimensionality reduction can alleviate computational load needed to process these data, in terms of both computing speed and memory usage. In this article, we present image reconstruction results from highly reduced radio-interferometric data, following our previously proposed data dimensionality reduction method, Rsing, based on studying the distribution of the singular values of the measurement operator. This method comprises a simple weighted, subsampled discrete Fourier transform of the dirty image. Additionally, we show that an alternative gridding-based reduction method works well for target data sizes of the same order as the image size. We reconstruct images from well-calibrated VLA data to showcase the robustness of our proposed method down to very low data sizes in a 'real data' setting. We show through comparisons with the conventional reduction method of time- and frequency-averaging, that our proposed method produces more accurate reconstructions while reducing data size much further, and is particularly robust when data sizes are aggressively reduced to low fractions of the image size. Rsing can function in a block-wise fashion, and could be used in the future to process incoming data by blocks in real-time, thus opening up the possibility of performing 'on-line' imaging as the data are being acquired. MATLAB code for the proposed dimensionality reduction method is available on GitHub.