Speckle is an inborn deformity caused by the interaction of backscattered waves from the target in active coherent imaging sensors such as synthetic aperture radar (SAR). Its presence severely limits the utility of SAR imagery in terms of detecting ground targets, retrieving information and analyzing scenes. The wavelet-based methods employ a threshold value on the noisy image for sparse wavelet representation. However, the noisy image coefficients exceeding the threshold are the cause of spurious noise spikes around the discontinuities. The edge preserving total variation (TV) regularizer is effective against speckle. Nevertheless, it is associated with staircase artifact. In this work, the wavelet-based forward model is integrated with a fractional order TV (FrTV) regularizer in the presence of a non-convex sparse prior to exploit the benefits of both methods. This combination aids in avoiding staircasing artifacts and preserving discontinuities while eliminating noise. Under some constraints, the optimization problem is convex, and it is solved using the alternating direction method of multipliers (ADMM). The alternating framework is iteratively solved by employing a thresholding operation, a shrinkage function, and quadratic minimization. The proposed method’s convergence is investigated both mathematically and empirically. The experimental results on both simulated and practical SAR data show that the proposed technique outperforms the previous algorithms in terms of speckle removal.