Limits...
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.

Show MeSH

Related in: MedlinePlus

Source overlap (SO, vertical axis) obtained by Lp-norm reconstruction (p = 1.5) for active sources with different extents (horizontal axis 1) in presence of white Gaussian noise with different SNR levels (horizontal axis 2).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3852818&req=5

fig5: Source overlap (SO, vertical axis) obtained by Lp-norm reconstruction (p = 1.5) for active sources with different extents (horizontal axis 1) in presence of white Gaussian noise with different SNR levels (horizontal axis 2).

Mentions: Next, we investigate the performance of our proposed Lp-norm regularization in presence of noise with different SNR levels (50–20 dB), using p = 1.5 as an example. Here we consider a region of size 1–52% of the left ventricle. As shown in Figure 5, increasing the noise level leads to minor decreasing of the OS value, and the trend of change is similar for sources of all sizes. The mean SO calculated for different source extents in presence of 50 dB noise is 0.35 and starts to decrease to 0.28, 0.25, and 0.2 as the SNR decreases to 40, 30, and 20, respectively. Again, the advantage of Lp regularization is more evident when the source is of medium size (~30% of LV).


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

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

Source overlap (SO, vertical axis) obtained by Lp-norm reconstruction (p = 1.5) for active sources with different extents (horizontal axis 1) in presence of white Gaussian noise with different SNR levels (horizontal axis 2).
© Copyright Policy
Related In: Results  -  Collection

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

fig5: Source overlap (SO, vertical axis) obtained by Lp-norm reconstruction (p = 1.5) for active sources with different extents (horizontal axis 1) in presence of white Gaussian noise with different SNR levels (horizontal axis 2).
Mentions: Next, we investigate the performance of our proposed Lp-norm regularization in presence of noise with different SNR levels (50–20 dB), using p = 1.5 as an example. Here we consider a region of size 1–52% of the left ventricle. As shown in Figure 5, increasing the noise level leads to minor decreasing of the OS value, and the trend of change is similar for sources of all sizes. The mean SO calculated for different source extents in presence of 50 dB noise is 0.35 and starts to decrease to 0.28, 0.25, and 0.2 as the SNR decreases to 40, 30, and 20, respectively. Again, the advantage of Lp regularization is more evident when the source is of medium size (~30% of LV).

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