Radar imaging is crucial in remote sensing and has many applications in detection and autonomous driving. However, the received radar signal for imaging is enormous and redundant, which degrades the speed of real-time radar quantitative imaging and leads to obstacles in the downlink applications. In this paper, we propose a physics-assisted deep learning method for radar quantitative imaging with the advantage of compressed sensing (CS). Specifically, the signal model for frequency-modulated continuous-wave (FMCW) radar imaging which only uses four antennas and parts of frequency components is formulated in terms of matrices multiplication. The learned fast iterative shrinkage-thresholding algorithm with residual neural network (L-FISTA-ResNet) is proposed for solving the quantitative imaging problem. The L-FISTA is developed to ensure the basic solution and ResNet is attached to enhance the image quality. Simulation results show that our proposed method has higher reconstruction accuracy than the traditional optimization method and pure neural networks. The effectiveness and generalization performance of the proposed strategy is verified in unseen target imaging, denoising, and frequency migration tasks.