Abstract Radio interferometers can achieve high spatial resolution for temporally constant sources by combining data observed over long periods of time. Recent imaging algorithms reconstruct smoothly varying sources by representing temporal variation in polynomial or Fourier bases. We present a novel image reconstruction algorithm that is able to reconstruct continuously and erratically varying sources as well, as long as they are confined to small regions of the image. This is achieved by enforcing spatial locality and sparsity of temporally varying sources through a group sparsity prior. Numerical experiments show that the proposed approach recovers image series to high accuracy where methods without temporal consistency fail, and outperforms static reconstructions of dynamic scenes even for image regions with no temporal variation.