Electromagnetic induction (EMI) sensors using sufficiently low-frequency harmonic sources and sufficiently small loop separations operate in the low-induction-number (LIN) domain for a relatively wide range of background conductivity. These systems are used in diverse near-surface investigations including applications from soil sciences, hydrology, and archaeology. The special case of portable multiconfiguration EMI sensors operating at frequencies offers the possibility of using a fast linear deconvolution method to interpret multichannel data sets in three dimensions. Here, we have developed a fast 3D inversion/deconvolution method regularized with 3D smoothness constraints and formulated in the hybrid spectral-spatial domain. Compared with other linear approaches, the spectral-spatial domain formulation significantly reduces the computational cost of the processing and opens the door for real-time 3D interpretation of large data sets consisting of more than 100,000 data points. First, we test our proposed algorithm on synthetic data sets computed with the full Maxwell theory. Then, we apply our method to a real four-configuration EMI data set acquired to map the thickness of peat layers embedded in a sandy environment. For the synthetic and the field example, we compared our result with the result obtained using a standard point-by-point 1D nonlinear inversion approach. This comparison demonstrates that the proposed methodology provides superior lateral resolution compared with the 1D nonlinear inversion, at the same time significantly reducing the computational cost of the processing.