To reduce the impact of attenuation and dispersion in ground penetrating radar (GPR) detection and to effectively improve GPR profile recording and to identify a weak detection target, a high-resolution processing method based on orthogonal matching pursuit and wavelet spectrum whitening (the OMWS method) is presented. First, according to the matching pursuit algorithm and the strong reflection-forming mechanism and based on sparse representation theory, a sparse dictionary suitable for the characteristics of a strong reflection signal was selected, and the signal was decomposed, which displayed the weak target signal well. Second, wavelet analysis was used to decompose the processed GPR signal into time-domain subsignals in different frequency bands, and each subsignal was whitened by a whitening filter. Then, the processed subsignals were reconstructed. The final results were compared with the results of conventional spectrum whitening method and showed that the OMWS method can accurately weaken the effect of the strong impedance interface and effectively enhance the local information of microcrack-reflected signals in both the time and frequency domains. The resolution of the processed GPR image is greatly improved, and the reflected signal of the hidden microcrack is easily visible. The method is clearer and more intuitive in the expression of the weak signals of hidden microcrack than the conventional spectrum whitening method, and the compensation for the high-frequency of the signals is more obvious.