<p>This study presents an advanced sparse deconvolution framework based on bivariate non-convex regularization, designed to detect sparse patterns in noisy or incomplete ground-penetrating radar (GPR) data. We propose an enhanced deconvolution framework specifically designed for GPR data. The framework provides a comprehensive evaluation of convex and non-convex regularization methods, focusing on penalty functions such as rational, arctangent, and logarithmic. Experimental results demonstrate that the proposed bivariate sparse regularization framework consistently outperforms conventional <i>ℓ</i>₁-norm methods, especially under high-noise conditions. The results, validated on both synthetic and real GPR datasets, reveal the superiority of the non-convex approach in achieving higher resolution and greater signal clarity. This work not only offers a thorough comparison of deconvolution techniques but also expands the application of bivariate sparse regularization to GPR, thereby enabling more accurate and interpretable subsurface imaging.</p>