Electrical impedance tomography (EIT) is highly affected by modeling errors regarding electrode positions and the shape of the imaging domain. In this work, we propose a new inclusion detection technique that is completely independent of such errors. Our new approach is based on a combination of frequency-difference and ultrasound modulated EIT measurements.

This study was conducted to evaluate the diagnostic performance of machine learning in differentiating follicular adenoma from carcinoma using preoperative ultrasonography (US). In this retrospective study, preoperative US images of 348 nodules from 340 patients were collected from two tertiary referral hospitals. Two experienced radiologists independently reviewed each image and categorized the nodules according to the 2015 American Thyroid Association guideline. Categorization of a nodule as highly suspicious was considered a positive diagnosis for malignancy. The nodules were manually segmented, and 96 radiomic features were extracted from each region of interest. Ten significant features were selected and used as final input variables in our in-house developed classifier models based on an artificial neural network (ANN) and support vector machine (SVM). The diagnostic performance of radiologists and both classifier models was calculated and compared. In total, 252 nodules from 245 patients were confirmed as follicular adenoma and 96 nodules from 95 patients were diagnosed as follicular carcinoma. As measures of diagnostic performance, the average sensitivity, specificity, and accuracy of the two experienced radiologists in discriminating follicular adenoma from carcinoma on preoperative US images were 24.0%, 84.0%, and 64.8%, respectively. The sensitivity, specificity, and accuracy of the ANN and SVM-based models were 32.3%, 90.1%, and 74.1% and 41.7%, 79.4%, and 69.0%, respectively. The kappa value of the two radiologists was 0.076, corresponding to slight agreement. Machine learning-based classifier models may aid in discriminating follicular adenoma from carcinoma using preoperative US.

A weighted‐norm least‐squares method is considered for the numerical approximation of solutions that have singularities at the boundary. While many methods suffer from a global loss of accuracy due to boundary singularities, the least‐squares method can be particularly sensitive to a loss of regularity. The method we describe here requires only a rough lower bound on the power of the singularity and can be applied to a wide range of elliptic equations. Optimal order discretization accuracy is achieved in weighted $H^1$, and functional norms and $L^2$ accuracy are retained for boundary value problems with a dominant div/curl operator. Our analysis, including interpolation bounds and several Poincaré‐type inequalities, are carried out in appropriately weighted Sobolev spaces. Numerical results confirm the error bounds predicted in the analysis.