This study aims to develop a silent, fast and 3D method for T1 and proton density (PD) mapping, while generating time series of T1-weighted (T1w) images with bias-field correction. Undersampled T1w images at different effective inversion times (TIs) were acquired using the inversion recovery prepared RUFIS sequence with an interleaved k-space trajectory. Unaliased images were reconstructed by constraining the signal evolution to a temporal subspace which was learned from the signal model. Parameter maps were obtained by fitting the data to the signal model, and bias-field correction was conducted on T1w images. Accuracy and repeatability of the method was accessed in repeated experiments with phantom and volunteers. For the phantom study, T1 values obtained by the proposed method were highly consistent with values from the gold standard method, R2 = 0.9976. Coefficients of variation (CVs) ranged from 0.09% to 0.83%. For the volunteer study, T1 values from gray and white matter regions were consistent with literature values, and peaks of gray and white matter can be clearly delineated on whole-brain T1 histograms. CVs ranged from 0.01% to 2.30%. The acoustic noise measured at the scanner isocenter was 2.6 dBA higher compared to the in-bore background. Rapid and with low acoustic noise, the proposed method is shown to produce accurate T1 and PD maps with high repeatability by reconstructing sparsely sampled T1w images at different TIs using temporal subspace. Our approach can greatly enhance patient comfort during examination and therefore increase the acceptance of the procedure.