The problem of phase unwrapping from a noisy and also incomplete wrapped phase map arises in many optics and image processing applications. In this work, we propose a noise-robust approach for processing regional phase dislocations. Our approach combines phase unwrapping and sparse-based inpainting with dictionary learning to recover the continuous phase map. The method is validated both using numerically simulated data with strong additive white Gaussian noise and phase dislocations; and experimental data from fringe projection profilometry. Comparisons with other phase inpainting method referred to as PULSI+INTERP, show the suitability of the proposed method for phase restoration even in extremely noisy phases. The error given by the proposed method on the highest level of noise (RMSE=0.0269 Rad) remains the smallest compared to the error given by PULSI+INTERP for noise-free data (RMSE=0.0332 Rad).