Deep unfolding for singular value decomposition compressed ghost imaging

The non-negativity of the measurement matrix in the traditional compressed ghost imaging system and iterative optimization process leads to low imaging quality and slow reconstruction speed. This paper proposes a singular value decomposition compressed ghost imaging method based on deep unfolding. The measurement matrix and training data pairs are generated through numerical simulation to reduces the cost of data acquisition. This paper adds a preprocessing layer to the network, which performs singular value decomposition on the measurement matrix to simultaneously obtain an optimized semi-orthogonal measurement matrix and optimized measurements. Then, iterative shrinking threshold algorithm network (ISTA-Net +) is used to learn the mapping between the measurements to the original signal from the training data set. Finally, the trained deep neural network can achieve non-iterative real-time reconstruction of high-quality images from low sampling rate measurements. Numerical experiments demonstrate that our proposed method has good reconstruction performance and good anti-noise performance at low sampling rates.