Deep Image Compressive Sensing Reconstruction Based on Range‒Null Space Decomposition

Image compressive sensing (ICS) reconstructs high-quality images from low-sampling observations. Applying deep learning to ICS significantly improves image reconstruction quality. However, deep learning-based ICS methods suffer from poor model interpretability and blind structural design, which degrade reconstruction performance. Therefore, a Range-Null Space Decomposition(RND)-based Deep Image Compressive Sensing Network is proposed, referred to as RND‒Net. This method sparsely senses image feature information through global convolutional sampling. Learning signal-related sampling matrices enables the sampling values to contain richer image features. Compared to common block-wise sampling methods, the global-level sampling approach remarkably reduces block artifacts. In addition, based on the mathematical representation of RND, the sampling and reconstruction processes are transformed into an end-to-end deep learning model. With the deep neural network fitting linear or nonlinear operations involved, model reasoning time is reduced, and image reconstruction ability is improved compared to traditional algorithms. This method, which effectively integrates mathematical prior knowledge into data-driven approaches, is called a collaborative driving method. It fully utilizes mathematical prior knowledge, strengthens model interpretability, simplifies model structure design, and uses the autonomous optimization capabilities of data-driven methods represented by deep learning. Compared to other deep compressive sensing methods, it more easily reaches the global optimal solution. Experiments on multiple test sets demonstrate that RND‒Net significantly improves image reconstruction quality and reduces the time required to reconstruct a single image compared to state-of-the-art algorithms. When the sampling rate is 0.1, and the test set is BSDS68, the average PSNR of RND‒Net is about 1.02 dB higher than that of AutoBCS. On Set14, the average PSNR and SSIM gains of RND‒Net over hybrid-driven GPX‒ADMM‒Net are 1.15 dB and 0.051 8, respectively. In addition, RND‒Net is about 0.104 9 s faster than GPX‒ADMM‒Net when reconstructing a single image.