Compressive sensing (CS)‐based image reconstruction methods have proposed random undersampling schemes that produce incoherent, noise‐like aliasing artifacts, which are easier to remove. The denoising process is critically assisted by imposing sparsity‐enforcing priors. Sparsity is known to be induced if the prior is in the form of the L_p (0 ≤ p ≤ 1) norm. CS methods generally use a convex relaxation of these priors such as the L₁ norm, which may not exploit the full power of CS. An efficient, discrete optimization formulation is proposed, which works not only on arbitrary L_p‐norm priors as some non‐convex CS methods do, but also on highly non‐convex truncated penalty functions, resulting in a specific type of edge‐preserving prior. These advanced features make the minimization problem highly non‐convex, and thus call for more sophisticated minimization routines.

中文翻译：

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一种基于字典的 MRI 重建图切割算法。

基于压缩感知 (CS) 的图像重建方法提出了随机欠采样方案，这些方案会产生不连贯的、类似噪声的混叠伪影，这些伪影更容易去除。去噪过程通过强加稀疏执行先验得到极大帮助。如果先验是L _p (0 ≤ p ≤ 1)范数的形式，则已知会引起稀疏性。CS 方法通常使用这些先验的凸松弛，例如L ₁范数，这可能无法利用 CS 的全部功能。提出了一种有效的离散优化公式，它不仅适用于任意L _p‐范数先验，就像一些非凸 CS 方法所做的那样，但也适用于高度非凸的截断惩罚函数，从而产生特定类型的边缘保留先验。这些高级特性使最小化问题高度非凸，因此需要更复杂的最小化例程。