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While tomographic imaging of cardiac structure and kinetics has improved substantially, electrophysiological mapping of the heart is still restricted to the surface with little or no depth information beneath. The progress in reconstructing 3-D action potential from surface voltage data has been hindered by the intrinsic ill-posedness of the problem and the lack of a unique solution in the absence of prior assumptions. In this work, we propose a novel adaption of the total-variation (TV) prior to exploit the unique spatial property of transmural action potential of being piecewise smooth with a steep boundary (gradient) separating depolarized and repolarized regions. We present a variational TV-prior instead of a common discrete TV-prior for improved robustness to mesh resolution, and solve the TV-minimization by a sequence of weighted, first-order L2-norm minimization. In a large set of phantom experiments, the proposed method is shown to outperform existing quadratic methods in preserving the steep gradient of action potential along the border of infarcts, as well as in capturing the disruption to the normal path of electrical wavefronts. Real-data experiments also further demonstrate the potential of the proposed method in revealing the location and shape of infarcts when quadratic methods fail to do so.

At present, denoising parameters in different signal processing algorithms require a specific signal waveform to be set. Human factors would significantly affect the denoising result. To solve this problem, we proposed a signal adaptive denoising method based on a denoising autoencoder to achieve denoising on ultrasonic signals. By applying this method to sample signals and comparing with the singular value decomposition (SVD), principal component analysis (PCA), and wavelet algorithms, it is found that this method can effectively suppress the noise at different noise intensities. Using the signal to noise ratio, root mean square error, and autocorrelation coefficient as evaluation parameters in the experiment, the overall denoising effect of the proposed method is better than that of PCA, and this method is better than the wavelet and SVD algorithms having a relatively weak noise intensity. In addition, by comparing the reconstructed signal curve of the proposed method and that of the wavelet algorithm, the proposed method can retain the information of signal saltation with a better performance. Finally, we apply this method for processing ultrasonic signals and verify its effectiveness from time and frequency domain diagrams.