For compressed sensing magnetic resonance imaging (CS-MRI) that utilize sparse representations, the regularization parameter establishes a trade-off between sparsity and data fidelity. While convergence to the desired solution is slow for mean squared error (MSE) optimal constant regularization, continuation using decreasing parameter values enables faster convergence. To derive an explicit rule for continuation, we propose an intermediate step optimization that involves maximization of the l2-norm of the gradient descent update. This is achieved by inclusion of an extra prior to the CS-MRI cost function. The solution is obtained using an alternating minimization approach in which the first sub-problem deals with the sparse regularization using the previously computed parameter value, and the second sub-problem aims at estimation of the parameter value to be used in the succeeding iteration. The solution to the second sub-problem is computed using standard root finding methods. Irrespective of the initial choice of the regularization parameter, we show that application of this continuation based proximal approach enables faster convergence to the desired solution.

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使用基于连续的近端方法的压缩传感 MRI 自动正则化参数选择

对于利用稀疏表示的压缩传感磁共振成像 (CS-MRI)，正则化参数建立了稀疏性和数据保真度之间的权衡。虽然均方误差 (MSE) 最优常数正则化对所需解的收敛速度较慢，但​​继续使用递减参数值可加快收敛速度​​。为了推导出一个明确的连续规则，我们提出了一个中间步骤优化，它涉及梯度下降更新的 l2 范数的最大化。这是通过在 CS-MRI 成本函数之前包含一个额外的东西来实现的。该解决方案是使用交替最小化方法获得的，其中第一个子问题使用先前计算的参数值处理稀疏正则化，第二个子问题旨在估计后续迭代中将使用的参数值。使用标准求根方法计算第二个子问题的解。不管正则化参数的初始选择如何，我们表明应用这种基于连续的近端方法可以更快地收敛到所需的解决方案。