Abstract: The sparse deconvolution method can recover more high-frequency components in seismic records compared to traditional linear deconvolution methods and is therefore widely used in practical applications. These methods exhibit poor robustness and limited recovery capability when processing weak reflection signals. By incorporating the piecewise concept of Huber constraints, an improved modified Cauchy sparse deconvolution method is proposed to enhance robustness. The proposed method adopts a piecewise constraint strategy to achieve differentiated sparse constraints for different types of signals: within the range above a set threshold, the expression of the modified Cauchy constraint is retained to fully exploit its advantage in weak reflection preservation; within the range below the threshold, an upper bound control is introduced to improve solution stability. The proposed method significantly enhances noise resistance while improving resolution, enabling relatively accurate and stable deconvolution results even under low signal-to-noise ratio conditions. Application to both synthetic and real seismic data demonstrates that the proposed method outperforms conventional methods in terms of robustness, resolution, and the recovery of weak reflection signals.