The random projections statistical technique has been used to reduce the dimensionality of the radiance data space generated from high spectral resolution infrared observations. The mathematical inversion of the physical radiative transfer equation for geophysical parameters has been solved in this space of reduced dimensionality. The great advantage of using random projections is that they provide an unified treatment of instrument noise and forward model error, which can be comprehensively modeled with a single variance term. The result is a novel retrieval approach, which combines computational efficiency to possibly improved accuracy of the retrieval products. The novel approach has been demonstrated through application to the Infrared Atmospheric Sounding Interferometer. We have found that state-of-the-art spectroscopy and related line-mixing treatment for the ν2CO2 absorption band, i.e., the fundamental band for temperature retrieval, show an excellent consistency with satellite observations.