The aim of this paper is to remove speckle noise and enhance the laminar bone structure in ultrasound images in order to aid the anesthesiologist during an epidural anesthesia needle insertion. In this regard, a direction and scale sensitive anisotropic diffusion (AD) algorithm called the complex wavelet diffusion algorithm is proposed. The proposed algorithm is tested on synthetic and real ultrasound images of the laminar bone and the results are compared with the speckle-reducing AD method. Results indicate that the proposed method can better highlight the diagonal-shaped laminar bones while removing speckle noise. Furthermore, the proposed despeckling algorithm is very fast providing the anesthesiologist with real-time information while an epidural injection is performed.