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We show that a single-cell spin-exchange relaxation-free (SERF) atomic magnetometer can be used for 3-D field measurements. The 3-D operation is achieved by optically pumping the magnetometer cell in successive layers perpendicular to the laser probe beam and by collecting the signals with a photodiode array. The vapor cell is thus divided into voxels acting as local atomic magnetometers. Each voxel's contribution to the probe linear polarization rotation is proportional to the convolution of the local polarization and the magnetic field. The layers are pumped in sequence without waiting for the atomic polarization in the previously pumped layer to relax to zero, consequently, reducing the total measurement time. The photodiode signals are the sum of accumulated linear polarization rotation caused by all the layers. These signals are processed by a deconvolution algorithm that extracts the information originating from each individual voxel. Our theoretical analysis and experimental results show that the time of a single-layer pumping can be reduced below the atomic-cell relaxation time constant, with almost no loss of precision.