Fast acquisition of MR images is possible through sparse encoding in the Fourier/Wavelet domain under the incoherent measurement constraint required by the theory of compressed sensing (CS) for stable reconstruction. In one such sparse encoding method, we utilize the wavelet tree structure to undersample the wavelet-encoded MRI k-spaces with tailored spatially-selective RF excitation pulses. The resulting undersampled k-spaces contain many more significant coefficients than randomly undersampled k-spaces. Thus, the quality of CS reconstruction based on these undersampled k-spaces is improved, and such an encoding scheme may reduce the patient scan time for MRI and fMRI. Using a fully sampled Fourier encoded 3-D digital brain phantom as the gold standard, a mathematical framework with full-reference and visual image quality matrices has been proposed to assess the CS reconstruction performance in wavelet-encoded MRI. The quality of MR images recovered from undersampled k-space by different reconstruction methods is computed. The undersampling rates and noise levels in k-space are considered in evaluating the robustness of CS reconstruction. The simulation results show that the performance of CS reconstruction in wavelet-encoded MRI is more accurate and stable than in Fourier-encoded MRI with the same undersampling rate and noise level, at a significantly reduced scan time.