Efficient Image Registration for Ultrasound Localization Microscopy by Obtaining Gradients via Integration Across Iterations

Tissue motion correction through image registration is essential for ultrasound localization microscopy (ULM). Parametric image registration is commonly formulated as an optimization problem where motion parameters are iteratively updated to maximize image similarity, and used optimization algorithms typically rely on gradient information, the explicit evaluation of which can become computationally demanding. This work investigates Extremum Seeking Control (ESC) as an alternative to explicit derivative evaluation in image registration. By obtaining descent information via integrating perturbed and demodulated image similarity metric across iterations, ESC avoids differentiation of the image similarity metric with respect to motion parameters in each iteration. The classical ESC, whose optimization behavior approximates that of classical gradient descent (GD), is first compared with GD for affine image registration using simulated ground-truth motions derived from a beating ex vivo porcine heart dataset. The results show that ESC achieves registration accuracy and convergence behavior comparable to GD while reducing per-iteration computational cost by approximately 3.5-fold. ESC is subsequently employed in a two-stage motion correction pipeline, where affine registration compensates for global tissue motion and B-spline registration corrects residual local deformation. The proposed method is applied to ULM imaging of a beating ex vivo porcine heart and achieves a spatial resolution of 219 um, substantially below the half-wavelength diffraction limit of 321 um associated with 2.4 MHz diverging-wave imaging. These results demonstrate that ESC provides an effective alternative to explicit derivative evaluation in ULM image registration, enabling accurate motion correction and high-quality super-resolution imaging.

Unsupervised High Impedance Fault Detection Using Autoencoder and Principal Component Analysis

Detection of high impedance faults (HIF) has been one of the biggest challenges in the power distribution network. The low current magnitude and diverse characteristics of HIFs make them difficult to be detected by over-current relays. Recently, data-driven methods based on machine learning models are gaining popularity in HIF detection due to their capability to learn complex patterns from data. Most machine learning-based detection methods adopt supervised learning techniques to distinguish HIFs from normal load conditions by performing classifications, which rely on a large amount of data collected during HIF. However, measurements of HIF are difficult to acquire in the real world. As a result, the reliability and generalization of the classification methods are limited when the load profiles and faults are not present in the training data. Consequently, this paper proposes an unsupervised HIF detection framework using the autoencoder and principal component analysis-based monitoring techniques. The proposed fault detection method detects the HIF by monitoring the changes in correlation structure within the current waveforms that are different from the normal loads. The performance of the proposed HIF detection method is tested using real data collected from a 4.16 kV distribution system and compared with results from a commercially available solution for HIF detection. The numerical results demonstrate that the proposed method outperforms the commercially available HIF detection technique while maintaining high security by not falsely detecting during load conditions.