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首页> 外文会议>Annual International Conference of the IEEE Engineering in Medicine and Biology Society >Unconstrained ℓ1 — regularized minimization with interpolated transformations for heart motion compensation
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Unconstrained ℓ1 — regularized minimization with interpolated transformations for heart motion compensation

机译：无约束ℓ 1 -带有插值变换的正则化最小化用于心脏运动补偿

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Motion compensation constitutes a challenging issue in minimally invasive beating heart surgery. Since the zone to be repaired has a dynamic behaviour, precision and surgeon's dexterity decrease. In order to solve this problem, various proposals have been presented using ℓ2-norm. However, as they present some limitations in terms of robustness and efficiency, motion compensation is still considered an open problem. In this work, a solution based on the class of ℓ1 Regularized Optimization is proposed. It has been selected due to its mathematical properties and practical benefits. In particular, deformation is characterized by cubic B-splines since they offer an excellent balance between computational cost and accuracy. Moreover, due to the non-differentiability of the functional, the logarithmic barrier function is used for generating a standard optimization problem. Results have provided a very good tradeoff between accuracy and efficiency, indicating the potential of the proposed approach and proving its stability even under complex deformations.
机译：运动补偿在微创跳动心脏手术中构成了一个具有挑战性的问题。由于要修复的区域具有动态行为，因此精度和外科医生的灵活性降低。为了解决这个问题，已经提出了使用ℓ2-范数的各种建议。但是，由于它们在鲁棒性和效率方面存在一些局限性，因此运动补偿仍然被认为是一个未解决的问题。在这项工作中，提出了一种基于ℓ1正则化优化类的解决方案。选择它是由于其数学特性和实际好处。尤其是，变形以三次B样条为特征，因为它们在计算成本和准确性之间提供了极好的平衡。此外，由于功能的不可微性，对数势垒函数用于生成标准优化问题。结果在精度和效率之间提供了很好的折衷，表明了该方法的潜力并证明了即使在复杂变形下的稳定性。

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