In this paper we present a novel method for multi-fiber reconstruction given a diffusion-weighted MRI dataset. There are several existing methods that employ various spherical deconvolution kernels for achieving this task. However the kernels in all of the existing methods rely on certain assumptions regarding the properties of the underlying fibers, which introduce inaccuracies and unnatural limitations in them. Our model is a non trivial generalization of the spherical deconvolution model, which unlike the existing methods does not make use of a fix-shaped kernel. Instead, the shape of the kernel is estimated simultaneously with the rest of the unknown parameters by employing a general adaptive model that can theoretically approximate any spherical deconvolution kernel. The performance of our model is demonstrated using simulated and real diffusion-weighed MR datasets and compared quantitatively with several existing techniques in literature. The results obtained indicate that our model has superior performance that is close to the theoretic limit of the best possible achievable result.