Abstract:  Linear frequency modulation continuous wave radar has some advantages like small size, low cost, anti-interception and so on, which gives it unique superiority in short-range imaging. However, LFMCW radar adopts Dechirp receiving system, so it strictly requires the frequency modulation linearity of the transmitted signal. In the real systems, the nonlinear frequency modulation will deteriorate the range compression result and affect the focusing effect. Because of the spatial variability of residual error after Dechirp, existing signal processing correction methods are difficult to balance the compensation accuracy and calculation efficiency. This paper first reveals the theoretical equivalence between the matched filtering and Dechirp processing. Then, using this equivalent principle, a space-varying error compensation method based on spectrum restoration is proposed. The new method restored the original echo spectrum by preprocessing the Dechirp signal, and then used the matched filtering for range compression processing, which can effectively avoid the error compensation of the spatial variability and realize the efficient and accurate correction of the nonlinear frequency modulation error. Finally, experimental results demonstrate the correctness of the theoretical analysis and the effectiveness of the proposed method.