In this paper, the inverse problem of reconstructing reflectivity function of a medium is examined within a blind deconvolution framework. The ultrasound pulse is estimated using higher-order statistics, and Wiener filter is used to obtain the ultrasonic reflectivity function through wavelet-based models. A new approach to the parameter estimation of the inverse filtering step is proposed in the nondestructive evaluation field, which is based on the theory of Fourier-Wavelet regularized deconvolution (ForWaRD). This new approach can be viewed as a solution to the open problem of adaptation of the ForWaRD framework to perform the convolution kernel estimation and deconvolution interdependently. The results indicate stable solutions of the estimated pulse and an improvement in the radio-frequency (RF) signal taking into account its signal-to-noise ratio (SNR) and axial resolution. Simulations and experiments showed that the proposed approach can provide robust and optimal estimates of the reflectivity function.