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A new approach to image reconstruction in magnetic resonance imaging is proposed using the mathematical model of singularity function analysis (SFA). Through this model, any discrete signal is expressed as a weighted sum of singularity functions. A layer extraction technique based on SFA is then developed to determine the singular points as well as the weighting coefficients from the acquired k-space data. Images are finally reconstructed using the obtained model parameters. This reconstruction methodology differs fundamentally from existing methods, and is particularly suitable for reconstructing images from truncated k-space. Experiments on both simulated and physical data revealed significant advantages of the present method over conventional reconstruction methods.