Within the TV framework there are several algorithms to restore images corrupted with Speckle (multiplicative) noise. Typically most of the methods convert the multiplicative model into an additive one by taking logarithms and can only handle the denoising case. By contrast, there are only a handful of algorithms that do not perform any conversion on the raw data and can handle the denoising and deconvolution cases, however their data fidelity term is non-convex. In this paper, we present a flexible and computationally efficient method to restore speckled grayscale/color images via a non-convex multiplicative model. The proposed algorithm uses a quadratic approximation of the data fidelity term to pose the original problem as a non-negative quadratic programming problem. Our experimental results for the denoising and deconvolution cases shows that the reconstruction quality of the proposed algorithm outperforms state of the art algorithms for speckled image restoration and at the same time offers competitive computational performance. © 2011 EURASIP.