Fully‐Constrained Variable Projection for Water‐Fat Models

PURPOSE: Variable projection (VARPRO) is an effective technique to reduce the dimensionality of least squares optimization problems through the elimination of linear parameters. For water-fat models, constrained VARPRO variants have been proposed in the literature to ensure that water and fat components are aligned at TE = 0, thereby preventing overfitting of data. These models, however, still allow for anti-parallel orientation of water and fat and therefore remain potentially vulnerable. An alternative, fully-constrained VARPRO formulation is derived, which resolves these limitations without compromising dimensionality reduction and/or numerical performance. THEORY AND METHODS: . RESULTS: becomes more stable using the proposed fully-constrained VARPRO method. CONCLUSION: Fully-constrained VARPRO enables more reliable local parameter estimation, while preserving the efficiency of existing approaches.