The inversion of seismic reflection data for acoustic impedance (AI) is a common and accepted method for the interpretation of poststack seismic data. The original mathematical problem is nonlinear due to the nonlinearity of relation between the AI and the earth reflectivity series and also the insufficiency of information about the source wavelet. Furthermore, the problem is ill posed due to the lack of low and high frequencies in the data. We have developed a multichannel blind inversion and solved it for obtaining the AI model and the wavelet directly from seismic reflection data. We found a solution to the overall problem by alternating between two subproblems, corresponding to the AI and wavelet recovery. Having an estimation of the wavelet, the algorithm directly inverts multichannel data for a high-resolution AI model, having blocky structures in the sense of total variation (TV) regularization, while satisfying a priori low-frequency information. The advantages of the split Bregman technique and the discrete cosine transform are used to build a fast and efficient algorithm for solving the nonlinear impedance inversion with TV regularization. Having an estimate of the AI model, the wavelet is updated by restricting it to have a sparse representation in a wavelet transformation domain while predicting the observed data. Numerical tests using simulated 2D data obtained from the benchmark Marmousi model and also 2D field data confirm that the proposed algorithm stably generates accurate estimates of complex AI models and complicated wavelets, simultaneously.