We propose a two-layer computational neuroscience model for storing and retrieving sensory patterns in memory. The first layer, sparse coding, generates condensed yet explicit representations adapted to the statistics of natural scenes. The second layer, a complex-valued associative memory model, can store patterns generated by the first layer and recover partial or corrupted versions of them. We demonstrate the model's collective effectiveness at denoising and recalling sensory patterns from a dataset of natural images, with both layers providing complementary contributions to improving the peak signal-to-noise ratio. In addition, the invariance of the model to pairwise phase differences allows for partial generalization to similar scenes. Collectively, these principles are consistent with prior theory and experiments in neuroscience, and lead to potential predictions about inference mechanisms in biological neural networks.