Image Volume Denoising Using a Fourier-wavelet Basis

A novel approach to the removal of noise from threedimensional image data is described. The image sequence is represented using a non-adaptive wavelet basis, carefully chosen for its ability to compactly represent locally planar surfaces. This is important in many 3-D applications, including video sequences, where they represent moving luminance edges, and medical volume data, where they represent the interfaces between tissue and bone, for example. The new basis, called a Fourier-Wavelet Basis, is an extension of the complex wavelet bases which have been increasing in popularity in recent years. Because transformation to the new basis is efficient computationally, the overall denoising algorithm is highly efficient. The success of the approach is demonstrated using a noisy video sequence and a noisy human knee MR image volume.