Spatial multifractal spectrum distribution method for breast ultrasonic image classification

The point-wise multifractal spectrum (MFS) of the ultrasonic image in the time-frequency domain is studied in this paper. With the theoretical derivation, the spatial multifractal spectrum (SMFS) distribution, as an extension of the conventional MFS, is proposed to analyze and characterize the spatial multiscale multifractal feature. Furthermore, the homogeneous region statistical MFS (HRS-MFS) with respect to different physical regions and the singularity-exponent-domain statistical multi-resolution (SSMR) feature image can be extracted from the renormalized SMFS data cube. The SMFS is rigorously derived from the two-dimensional multifractal spectrum and the Pseudo Wigner-Ville distribution (PWVD). In addition, both the SSMR feature images based on the SMFS and the singularity exponent of the 2D-PWVD is proved to be the SNR independence in the Gaussian white noise (GWN) background, which ensures the robust estimation of SMFS features of images under low SNR conditions. Furthermore, the HRS-MFS and the SSMR feature images of the breast ultrasound images (BUSI) are extracted to discriminate the specificity of the tumor regions. Then, a novel BUSI classification method based on the SMFS and deep learning network is proposed and tested on the public BUSI datasets. The experiment results indicate that the SMFS method can significantly reduce the risk of the 'intermediate effects'. In fact, the classification accuracy of the original deep network is considerately improved by 9.3 % with the SMFS method, and 94.8 % classification accuracy is achieved, which is superior by 3.3 % to the state-of-art method.