Improvements in the accuracy of wavelet-based optical flow velocimetry (wOFV) using an efficient and physically based implementation of velocity regularization

This manuscript details recent improvements in a wavelet-based optical flow velocimetry (wOFV) method that represents a more physically sound implementation and results in increased accuracy of the velocity estimation. A novel regularization scheme is presented that is based on penalization of directional derivatives of the estimated velocity field or more specifically, second-order penalization of the gradients of divergence and curl, which enforces realistic flow structure. The regularization is performed in the wavelet domain with symmetric boundary conditions for the first time using an alternative wavelet transform approach of matrix multiplications. The method for the computation of full two-dimensional wavelet transforms by a single pair of matrix multiplications is described and shown to be significantly more efficient than a lifting implementation or convolution in MATLAB. Velocity fields are estimated from synthetic tracer particle images generated from 2D DNS of isotropic turbulence and from experimental results from a turbulent flow. Results are compared to an advanced correlation-based PIV algorithm and previous advanced optical flow methods. The velocity results estimated with the new regularization scheme are shown to be more accurate and exhibit a significant reduction in non-physical small-scale artifacts compared to previous results. A significant result from the current method is the ability to generate 2D velocity field images that resolve the dissipative scales in high-Reynolds number, turbulent flows.