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Abstract This work is concerned with optical imaging in strongly diffusive environments. We consider a typical setting in optical coherence tomography where a sample is probed by a collection of wavefields produced by a laser and propagating through a microscope. We operate in a scenario where the illuminations are in a speckle regime, namely fully randomized. This occurs when the light propagates deep in highly heterogeneous media. State-of-the-art coherent techniques are based on the ballistic part of the wavefield, that is the fraction of the wave that propagates freely and decays exponentially fast. In a speckle regime, the ballistic field is negligible compared to the scattered field, which precludes the use of coherent methods and different approaches are needed. We propose a new strategy based on blind source separation and total variation deconvolution to obtain images with diffraction-limited resolution. The source separation allows us to isolate the fields diffused by the different scatterers to be imaged, while the deconvolution exploits the speckle memory effect to estimate the relative position of these scatterers. Our method is validated with numerical simulations and is shown to be effective not only for imaging discrete scatterers, but also continuous objects.