prewhiten

Prewhiten is a term used in signal processing and image processing to describe a transformation applied to data. The goal of prewhitening is to decorrelate the data and normalize its variance, making it more suitable for subsequent analysis or algorithms. In essence, it attempts to remove correlations between different features or channels of the data and make their variances equal.

This process is often applied to time series data or images before applying techniques such as Principal Component Analysis (PCA) or Independent Component Analysis (ICA). By prewhitening the data, the assumption of uncorrelated or independent components in these algorithms is better met, leading to more accurate and meaningful results. For example, in image processing, prewhitening can be used to correct for the color correlations present in natural images.

Mathematically, prewhitening typically involves a linear transformation of the data. This transformation is derived from the covariance matrix of the data. One common method involves applying a transformation matrix that effectively rotates and scales the data. After prewhitening, the covariance matrix of the transformed data is the identity matrix, indicating that all components are uncorrelated and have unit variance. This simplification can significantly improve the performance and interpretability of many data analysis techniques.