We introduce a PDE-free variational model for multiphase image segmentation that uses a sparse representation basis (wavelets or other) instead of a Fourier basis in a modified diffuse interface context. The segmentation model we present differs from other state-of-the-art models in several ways. The diffusive nature of the method originates from the sparse representations and thus propagates information in a different manner comparing to any existing PDE models, even though it still has such classical features as coarsening and phase separation. The model has a non-local nature, yet with much reduced diffuse interface blur, thus allowing to connect important features and preserve sharp edges in the output. Numerical experiments show that the method is robust to noise and is highly tunable.