A method for reconstructing magnetic resonance imaging data includes acquiring a measurement dataset using a magnetic resonance imaging device and determining an estimated image dataset based on the measurement dataset. An iterative reconstruction process is performed to refine the estimated image dataset. Each iteration of the iterative reconstruction process comprises: updating the measurement dataset and a sparse coefficient dataset based on the estimated image dataset and a plurality of belief propagation terms, incorporating a noise prior dataset into the measurement dataset, incorporating a sparsity prior dataset into the sparse coefficient dataset, updating the plurality of belief propagation terms based on the measurement dataset and the sparsity prior dataset, and updating the estimated image dataset based on the plurality of belief propagation terms. A reconstructed image and confidence map are generated using the estimated image dataset.