Space-Frequency Weighting of Brushlet Transform for Texture Representation in 3D Medical Imaging

Brushlet expansion based texture representation is an effective tool due to complete partitioning of Fourier space via Space-Frequency Blocks (SFBs), possibility of arbitrary orientation selection and reduced redundancy by utilization of orthogonal basis. It is also shown that reconstruction only with user selected SFBs can enhance desired information. In parallel with these studies, the importance of generating multi-scale combinations of basis functions for texture characterization has been emphasized. Existing approaches use machine learning to find weighted combination of filters inside a predefined set, such that the difference between desired texture and obtained signature is minimized. In this paper, instead of using a limited filter bank, the optimal weights of SFBs in an expansion are determined to extract a desired texture. Accordingly, a novel method is proposed for reconstruction with optimally weighted SFBs. Applications show that proposed learning strategy converges for desired texture patterns and successful extraction can be achieved. Moreover, SFB weighting is shown to outperform SFB selection when 3D visualization of liver from computed tomography is considered.