Naveed Naimipour

Naveed Naimipour, Shahin Khobahi, Mojtaba Soltanalian

Exploring the idea of phase retrieval has been intriguing researchers for decades, due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phaseless measurements. In this paper, we approach the problem by proposing a hybrid model-based data-driven deep architecture, referred to as Unfolded Phase Retrieval (UPR), that exhibits significant potential in improving the performance of state-of-the art data-driven and model-based phase retrieval algorithms. The proposed method benefits from versatility and interpretability of well-established model-based algorithms, while simultaneously benefiting from the expressive power of deep neural networks. In particular, our proposed model-based deep architecture is applied to the conventional phase retrieval problem (via the incremental reshaped Wirtinger flow algorithm) and the sparse phase retrieval problem (via the sparse truncated amplitude flow algorithm), showing immense promise in both cases. Furthermore, we consider a joint design of the sensing matrix and the signal processing algorithm and utilize the deep unfolding technique in the process. Our numerical results illustrate the effectiveness of such hybrid model-based and data-driven frameworks and showcase the untapped potential of data-aided methodologies to enhance the existing phase retrieval algorithms.

Naveed Naimipour, Shahin Khobahi, Mojtaba Soltanalian

The problem of phase retrieval has been intriguing researchers for decades due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phase-less measurements. In this paper, we approach the problem by proposing a hybrid model-based data-driven deep architecture, referred to as the Unfolded Phase Retrieval (UPR), that shows potential in improving the performance of the state-of-the-art phase retrieval algorithms. Specifically, the proposed method benefits from versatility and interpretability of well established model-based algorithms, while simultaneously benefiting from the expressive power of deep neural networks. Our numerical results illustrate the effectiveness of such hybrid deep architectures and showcase the untapped potential of data-aided methodologies to enhance the existing phase retrieval algorithms.

Shahin Khobahi, Naveed Naimipour, Mojtaba Soltanalian et al.

Machine learning, and more specifically deep learning, have shown remarkable performance in sensing, communications, and inference. In this paper, we consider the application of the deep unfolding technique in the problem of signal reconstruction from its one-bit noisy measurements. Namely, we propose a model-based machine learning method and unfold the iterations of an inference optimization algorithm into the layers of a deep neural network for one-bit signal recovery. The resulting network, which we refer to as DeepRec, can efficiently handle the recovery of high-dimensional signals from acquired one-bit noisy measurements. The proposed method results in an improvement in accuracy and computational efficiency with respect to the original framework as shown through numerical analysis.