Temporal super-resolution of echocardiography using a novel high-precision non-polynomial interpolation

Higher frame rates are very useful for improving medical diagnosis in fast-moving parts of the heart, especially in the valves. To this end, we propose a non-polynomial interpolation method for increasing the frame rate in echocardiography. Besides describing the proposed method, we present two additional contributions: (1) we obtain a closed-form solution, which is continuous and infinitely differentiable; (2) we provide an error analysis of the method. The resulting error bound indicates that the interpolation method is reliable. Finally, to show the efficiency of our proposal in temporal super-resolution, i.e., the increase in frame rate, we apply it to three types of datasets, including a 1D signal, a simulated dataset, and B-mode echocardiography images. Our experimental results show that the Mean Squared Error of the proposed method is reduced from 0.6 to 0.3, while having the same computational complexity compared to cubic B-spline. The quantitative results also indicate that, even with lower selection rates, we can reach a high performance reconstruction while the image quality is not degraded significantly.