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Purpose: To develop SPARCQ (Signal Profile Asymmetries for Rapid Compartment Quantification), a novel approach to quantify fat fraction using asymmetries in the phase-cycled bSSFP profile. Methods: SPARCQ uses phase-cycling to obtain bSSFP frequency profiles, which display asymmetries in the presence of fat and water at certain repetition times. For each voxel, the measured signal profile is decomposed into a weighted sum of simulated profiles via multi-compartment dictionary matching. Each dictionary entry represents a single-compartment bSSFP profile with a specific off-resonance frequency and relaxation time ratio. Using the results of dictionary matching, the fractions of the different off-resonance components are extracted for each voxel, generating quantitative maps of water and fat fraction and banding-artifact-free images for the entire image volume. SPARCQ was validated using simulations, experiments in a water-fat phantom and in knees of healthy volunteers. Experimental results were compared with reference proton density fat fractions obtained with 1H-MRS (phantoms) and with multiecho gradient-echo MRI (phantoms and volunteers). SPARCQ repeatability was evaluated in six scan-rescan experiments. Results: Simulations showed that fat fraction quantification is accurate and robust for signal-to-noise ratios greater than 20. Phantom experiments demonstrated good agreement between SPARCQ and gold standard fat fractions. In volunteers, banding-artifact-free quantitative maps and water-fat-separated images obtained with SPARCQ and ME-GRE demonstrated the expected contrast between fatty and non-fatty tissues. The coefficient of repeatability of SPARCQ fat fraction was 0.0512. Conclusion: SPARCQ demonstrates potential for fat quantification using asymmetries in bSSFP profiles, and may be a promising alternative to conventional fat fraction quantification techniques.