As an emerging signal acquisition framework, compressed sensing theory breaks through the limitations of traditional Nyquist sampling. It utilizes the sparsity prior of the signal and only collects a small number of linear projection values to reconstruct the original signal with high probability through nonlinear reconstruction algorithms. This study aims to explore the application of compressed sensing theory in the field of image restoration and reconstruction, including image reconstruction of ultra-fast compressed imaging and 3D image reconstruction from a very small number of projection angles. The numerical experimental results show that the image restoration and reconstruction technology based on compressed sensing can significantly reduce the sampling requirements, and can effectively reconstruct high-quality images even with only partial sampling data.