Infrared hyperspectral imaging is a powerful approach in the field of materials and life sciences. However, the extension to modern sub-diffraction nanoimaging still remains a highly inefficient technique, as it acquires data via inherent sequential schemes. Here, we introduce the mathematical technique of low-rank matrix reconstruction to the sub-diffraction scheme of atomic force microscopy-based infrared spectroscopy (AFM-IR), for efficient hyperspectral infrared nanoimaging. To demonstrate its application potential, we chose the trypanosomatid unicellular parasites Leishmania species as a realistic target of biological importance. The mid-infrared spectral fingerprint window covering the spectral range from 1300 to 1900 cm$^{-1}$ was chosen and a step width of 220 nm was applied for nanoimaging of single parasites. Multivariate statistics approaches such as hierarchical cluster analysis (HCA) were used for extracting the chemically distinct spatial locations. Subsequently, we randomly selected only 5% from an originally gathered data cube of 134 (x) $\times$ 50 (y) $\times$ 148 (spectral) AFM-IR measurements and reconstructed the full data set by low-rank matrix recovery. The technique is evaluated by showing agreement in the cluster regions between full and reconstructed data cubes. We conclude that the corresponding measurement time of more than 14 hours can be reduced to less than 1 hour. These findings can significantly boost the practical applicability of hyperspectral nanoimaging in both academic and industrial settings involving nano- and bio-materials.
