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Lp-norm regularization in volumetric imaging of cardiac current sources.

Rahimi A, Xu J, Wang L - Comput Math Methods Med (2013)

Bottom Line: Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart.In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents.This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation.

View Article: PubMed Central - PubMed

Affiliation: Rochester Institute of Technology, Rochester, NY 14623, USA.

ABSTRACT
Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart. In comparison, our ability to observe and analyze cardiac electrical activities is much limited. The progress to computationally reconstruct cardiac current sources from noninvasive voltage data sensed on the body surface has been hindered by the ill-posedness and the lack of a unique solution of the reconstruction problem. Common L2- and L1-norm regularizations tend to produce a solution that is either too diffused or too scattered to reflect the complex spatial structure of current source distribution in the heart. In this work, we propose a general regularization with Lp-norm (1 < p < 2) constraint to bridge the gap and balance between an overly smeared and overly focal solution in cardiac source reconstruction. In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents. Through computer-simulated and real-data experiments, we further demonstrate the feasibility of the proposed method in imaging the complex structure of excitation wavefront, as well as current sources distributed along the postinfarction scar border. This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation.

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Related in: MedlinePlus

(a) Source overlap (SO, vertical axis) obtained by Lp-norm reconstruction (1 ≤ p ≤ 2, horizontal axis 1) for active sources with different extents (ranging from 1 to more than 80 active sources in the region, horizontal axis 2). (b)–(d) Examples of SO mean and standard deviation obtained by Lp-norm reconstruction (1 ≤ p ≤ 2) for a region of (b) 1–10, (c) 20–30, and (d) 40–50 active sources.
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fig4: (a) Source overlap (SO, vertical axis) obtained by Lp-norm reconstruction (1 ≤ p ≤ 2, horizontal axis 1) for active sources with different extents (ranging from 1 to more than 80 active sources in the region, horizontal axis 2). (b)–(d) Examples of SO mean and standard deviation obtained by Lp-norm reconstruction (1 ≤ p ≤ 2) for a region of (b) 1–10, (c) 20–30, and (d) 40–50 active sources.

Mentions: Figure 4(a) summarizes the mean SO (vertical axis) between the true and estimated source regions obtained using Lp-norm regularization, as p increases from 1 to 2 (horizontal axis 1) and as the size of active region increases (horizontal axis 2). As shown, for source regions of all sizes, similar trend of SO change can be observed as p increases from 1 to 2 in the Lp-norm regularization: the sparse solution produced by L1-norm regularization, though produces low false-positives, also has a high underestimation (low numerator in the calculation of the OS) and therefore a low value of OS. On the other extreme, the smeared solution of L2-norm regularization, though is able to detect the majority of the true active sources, tends to have a high overestimation (high denominator in the calculation of the OS) and thus leads to again a low OS value. Therefore, for source region of all sizes (as the 3 examples shown in Figures 4(b)–4(d)), we can observe an increase followed by a decrease of the OS value when p increases from 1 to 2, with the maximum OS obtained when 1.5 ≤ p ≤ 1.6. Such benefits of the Lp-norm regularization with 1 < p < 2 are particularly evident when the source region is of medium size (≤30% of the left ventricle).


Lp-norm regularization in volumetric imaging of cardiac current sources.

Rahimi A, Xu J, Wang L - Comput Math Methods Med (2013)

(a) Source overlap (SO, vertical axis) obtained by Lp-norm reconstruction (1 ≤ p ≤ 2, horizontal axis 1) for active sources with different extents (ranging from 1 to more than 80 active sources in the region, horizontal axis 2). (b)–(d) Examples of SO mean and standard deviation obtained by Lp-norm reconstruction (1 ≤ p ≤ 2) for a region of (b) 1–10, (c) 20–30, and (d) 40–50 active sources.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3852818&req=5

fig4: (a) Source overlap (SO, vertical axis) obtained by Lp-norm reconstruction (1 ≤ p ≤ 2, horizontal axis 1) for active sources with different extents (ranging from 1 to more than 80 active sources in the region, horizontal axis 2). (b)–(d) Examples of SO mean and standard deviation obtained by Lp-norm reconstruction (1 ≤ p ≤ 2) for a region of (b) 1–10, (c) 20–30, and (d) 40–50 active sources.
Mentions: Figure 4(a) summarizes the mean SO (vertical axis) between the true and estimated source regions obtained using Lp-norm regularization, as p increases from 1 to 2 (horizontal axis 1) and as the size of active region increases (horizontal axis 2). As shown, for source regions of all sizes, similar trend of SO change can be observed as p increases from 1 to 2 in the Lp-norm regularization: the sparse solution produced by L1-norm regularization, though produces low false-positives, also has a high underestimation (low numerator in the calculation of the OS) and therefore a low value of OS. On the other extreme, the smeared solution of L2-norm regularization, though is able to detect the majority of the true active sources, tends to have a high overestimation (high denominator in the calculation of the OS) and thus leads to again a low OS value. Therefore, for source region of all sizes (as the 3 examples shown in Figures 4(b)–4(d)), we can observe an increase followed by a decrease of the OS value when p increases from 1 to 2, with the maximum OS obtained when 1.5 ≤ p ≤ 1.6. Such benefits of the Lp-norm regularization with 1 < p < 2 are particularly evident when the source region is of medium size (≤30% of the left ventricle).

Bottom Line: Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart.In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents.This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation.

View Article: PubMed Central - PubMed

Affiliation: Rochester Institute of Technology, Rochester, NY 14623, USA.

ABSTRACT
Advances in computer vision have substantially improved our ability to analyze the structure and mechanics of the heart. In comparison, our ability to observe and analyze cardiac electrical activities is much limited. The progress to computationally reconstruct cardiac current sources from noninvasive voltage data sensed on the body surface has been hindered by the ill-posedness and the lack of a unique solution of the reconstruction problem. Common L2- and L1-norm regularizations tend to produce a solution that is either too diffused or too scattered to reflect the complex spatial structure of current source distribution in the heart. In this work, we propose a general regularization with Lp-norm (1 < p < 2) constraint to bridge the gap and balance between an overly smeared and overly focal solution in cardiac source reconstruction. In a set of phantom experiments, we demonstrate the superiority of the proposed Lp-norm method over its L1 and L2 counterparts in imaging cardiac current sources with increasing extents. Through computer-simulated and real-data experiments, we further demonstrate the feasibility of the proposed method in imaging the complex structure of excitation wavefront, as well as current sources distributed along the postinfarction scar border. This ability to preserve the spatial structure of source distribution is important for revealing the potential disruption to the normal heart excitation.

Show MeSH
Related in: MedlinePlus