Tree Search Network for Sparse Regression

We consider the classical sparse regression problem of recovering a sparse signal $x_0$ given a measurement vector $y = \Phi x_0+w$. We propose a tree search algorithm driven by the deep neural network for sparse regression (TSN). TSN improves the signal reconstruction performance of the deep neural network designed for sparse regression by performing a tree search with pruning. It is observed in both noiseless and noisy cases, TSN recovers synthetic and real signals with lower complexity than a conventional tree search and is superior to existing algorithms by a large margin for various types of the sensing matrix $\Phi$, widely used in sparse regression

Fourier Phase Retrieval with Extended Support Estimation via Deep Neural Network

We consider the problem of sparse phase retrieval from Fourier transform magnitudes to recover the $k$-sparse signal vector and its support $\mathcal{T}$. We exploit extended support estimate $\mathcal{E}$ with size larger than $k$ satisfying $\mathcal{E} \supseteq \mathcal{T}$ and obtained by a trained deep neural network (DNN). To make the DNN learnable, it provides $\mathcal{E}$ as the union of equivalent solutions of $\mathcal{T}$ by utilizing modulo Fourier invariances. Set $\mathcal{E}$ can be estimated with short running time via the DNN, and support $\mathcal{T}$ can be determined from the DNN output rather than from the full index set by applying hard thresholding to $\mathcal{E}$. Thus, the DNN-based extended support estimation improves the reconstruction performance of the signal with a low complexity burden dependent on $k$. Numerical results verify that the proposed scheme has a superior performance with lower complexity compared to local search-based greedy sparse phase retrieval and a state-of-the-art variant of the Fienup method