Breast volume denoising and noise characterization by 3D wavelet transform.

Breast imaging through cone-beam computed tomography provides a digital breast volume, with which the three-dimensional (3D) breast tissues can be analyzed. Data denoising, as a preprocessing step for subsequent volumetric breast segmentation is always needed. In this paper, we report a volumetric denoising technique by a separable 3D wavelet transform (WT), i.e. a '2D WT plus 1D WT' scheme. Specifically, the scheme performs two-dimensional (2D) wavelet denoising on a stack of slice images of the breast volume, followed by one-dimensional (1D) wavelet denoising along the stacking direction. The denoising is achieved by wavelet decomposition, high-pass subband attenuation, and wavelet synthesis. A one-level 3D WT produces eight subbands occupying the octants of the 3D wavelet space. Multilevel WT also provides a multiresolution representation of breast volume, i.e. a sequence of low-pass subbands. In general, most noise and irregularity features are imparted into the high-pass subbands, which are removed or reduced for denoising purpose. Meanwhile, the information in a subband can be characterized in terms of energy, variance, and entropy. Through 3D visualization, the spatial structure in a subband can also be visually perceived. Experimental demonstration with the breast volume reconstructed from a specimen is provided.