Fig. 1.

Visualization of DFW basis functions. a: Linear and quadratic spline scaling function ϕ(x) and wavelet function ψ(x) that are used to construct DFWs. ϕ₀, ψ₀ and ϕ₁, ψ₁ are related by differentiation, thereby enabling the construction of DFWs. b: Examples of divergence-free components of DFW basis functions. c: Examples of nondivergence-free components of DFW basis functions. d: Flow diagram of DFW denoising. The entire procedure consists of applying separate wavelet transforms on each velocity component and linearly combine the coefficients, which achieves linear computational complexity overall. (FWT: forward wavelet transform, IWT: inverse wavelet transform, wc: wavelet coefficient, df: divergence-free, n: nondivergence-free). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]