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This study describes a new approach to reconstruct data that has been corrupted by unfavorable magnetization evolution. In this new framework, images are reconstructed in a weighted least squares fashion using all available data and a measure of consistency determined from the data itself. The reconstruction scheme optimally balances uncertainties from noise error with those from data inconsistency, is compatible with methods that model signal corruption, and may be advantageous for more accurate and precise reconstruction with many least squares-based image estimation techniques including parallel imaging and constrained reconstruction/compressed sensing applications. Performance of the several variants of the algorithm tailored for fast spin echo and self-gated respiratory gating applications was evaluated in simulations, phantom experiments, and in vivo scans. The data consistency weighting technique substantially improved image quality and reduced noise as compared to traditional reconstruction approaches.