In the context of multivariate curve resolution (MCR) and spectral unmixing, essential information (EI) corresponds to the most linearly dissimilar rows and/or columns of a two-way data matrix. In recent works, the assessment of EI has been revealed to be a very useful practical tool to select the most relevant spectral information before MCR analysis, key features being speed and compression ability. However, the canonical approach relies on the principal component analysis to evaluate the convex hull that encapsulates the data structure in the normalized score space. This implies that the evaluation of the essentiality of each spectrum can only be achieved after all the spectra have been acquired by the instrument. This paper proposes a new approach to extract EI in the Fourier domain (EIFD). Spectral information is transformed into Fourier coefficients, and EI is assessed from a convex hull analysis of the data point cloud in the 2D phasor plots of a few selected harmonics. Because the coordinate system of a phasor plot does not depend on the data themselves, the evaluation of the essentiality of the information carried by each spectrum can be achieved individually and independently from the others. As a result, time-consuming operations like Raman spectral imaging can be significantly accelerated exploiting a chemometric-driven (i.e., based on the EI content of a spectral pixel) procedure for data acquisition and targeted sampling. The usefulness of EIFD is shown by analyzing Raman hyperspectral microimaging data, demonstrating a potential 50-fold acceleration of Raman acquisition.