Digital speckle pattern interferometry (DSPI) is a widely used technique in various high-precision nondestructive testing applications. However, a coherence multiplicative noise, called speckle noise, is produced. Speckle noise degrades the quality and the resolution of the fringes, leading to difficulties in fringe analysis and phase retrieval. We aim to restore the DSPI correlation fringes and reduce the speckle noise through a multidirectional total variation method. In this method, the local fringe orientation, computed through Riesz transform, is used to increase the sensitivity of the variational regularization to the spatially varying directional intensity changes. The proposed algorithm is applied to the directional wavelet phase retrieval technique. The performance of the proposed method is evaluated with both simulated and experimental DSPI fringe patterns, obtaining satisfactory results.