Quantitative Susceptibility Mapping is a parametric imaging technique to estimate the magnetic susceptibilities of biological tissues from MRI phase measurements. This problem of estimating the susceptibility map is ill posed. Regularized recovery approaches exploiting signal properties such as smoothness and sparsity improve reconstructions, but suffer from over-smoothing artifacts. Deep learning approaches have shown great potential and generate maps with reduced artifacts. However, for reasonable reconstructions and network generalization, they require numerous training datasets resulting in increased data acquisition time. To overcome this issue, we proposed a subject-specific, patch-based, unsupervised learning algorithm to estimate the susceptibility map. We improved the conditioning of the problem by exploiting the redundancies across the patches of the map using a deep convolutional neural network. We formulated the recovery of the susceptibility map as a regularized optimization problem and adopted an alternating minimization strategy to solve it. We tested the algorithm on a 3D invivo dataset and, qualitatively and quantitatively, demonstrated improved reconstructions over competing methods.