Coupling 2D‐wavelet decomposition and multivariate image analysis (2D WT‐MIA)

The use of 2D discrete wavelet transform in the feature enhancement phase of multivariate image analysis is discussed and implemented in a comparative way with respect to previous publications. In the proposed approach, all the resulting subimages obtained by discrete wavelet transform decomposition are unfolded pixel‐wise and midlevel data fused to a feature matrix that is used for the feature analysis phase. Congruent subimages can be obtained either by reconstruction of each decomposition block to the original pixel dimensions or by using the stationary wavelet transform decomposition scheme. The main advantage is that all possible relationships among blocks, decomposition levels, and channels are assessed in a single multivariate analysis step (feature analysis). This is particularly useful in a monitoring context where the aim is to build multivariate control charts based on images. Moreover, the approach can be versatile for contexts where several images are analyzed at a time as well as in the multispectral image analysis. Both a set of simple artificial images and a set of real images, representative of the on‐line quality monitoring context, will be used to highlight the details of the methodology and show how the wavelet transform allows extracting features that are informative of how strong the texture of the image is and in which direction it varies. 2D Wavelet Transform (DWT or SWT) in the Feature Enhancement phase of Multivariate Image Analysis is compared to current state of art. Wavelet‐decomposition images are unfolded pixel‐wise and mid‐level datafused to a Feature Matrix so that all relationships among blocks, decomposition levels and channels are assessed in a single multivariate Feature Analysis step. The approach is suitable in process monitoring context. Also, denoising and background removal are obtained at WT decomposition stage, and it can be easily extended to hyperspectral images.