Deep convolutional robust PCA with application to ultrasound imaging

Sparse and low-rank decomposition, also known as robust principle component analysis, has been applied successfully in numerous applications. Typically, this approach leads to a minimization problem which is solved using iterative algorithms. Drawing inspiration from recurrent networks, in recent years deep-learning strategies have been extended to mimic the behavior of iterative algorithms, with reduced complexity. In this work, we propose an extension of these deep architectures to robust principle component analysis in which fully-connected layers are replaced with convolutional ones. This strategy offers spatial invariance and significant reduction in the number of learned parameters. We then apply the proposed method to contrast-enhanced ultrasound, in which low-rank tissue signal needs to be removed in order to visualize blood vessels. We demonstrate the effectiveness of our approach on simulations and in-vivo rat brain scans. The resulting images exhibit improved visual quality and contrast compared with images obtained by commonly practiced methods.