Speckle artifacts can strongly hamper quantitative analysis of optical coherence tomography (OCT), which is necessary to provide assessment of ocular disorders associated with vision loss. Here, we introduce a method for speckle reduction, which leverages from low-rank + sparsity decomposition (LRpSD) of the logarithm of intensity OCT images. In particular, we combine nonconvex regularization-based low-rank approximation of an original OCT image with a sparsity term that incorporates the speckle. State-of-the-art methods for LRpSD require a priori knowledge of a rank and approximate it with nuclear norm, which is not an accurate rank indicator. As opposed to that, the proposed method provides more accurate approximation of a rank through the use of nonconvex regularization that induces sparse approximation of singular values. Furthermore, a rank value is not required to be known a priori. This, in turn, yields an automatic and computationally more efficient method for speckle reduction, which yields the OCT image with improved contrast-to-noise ratio, contrast and edge fidelity. The source code will be available at www.mipav.net/English/research/research.html.