MATLAB Implementation of Wavelet Transform-Based Principal Component Analysis for Face Recognition

Principal Component Analysis (PCA) combined with wavelet transform has broad applications in face recognition. Below is a MATLAB-based implementation example demonstrating this methodology. The program workflow consists of four key phases: First, the face image dataset is loaded and preprocessed using functions like imread() and rgb2gray() for standardization. Image resizing and normalization are typically performed to ensure dimensional consistency. Second, 2D discrete wavelet transform (DWT) is applied using wavelet families (e.g., 'db1' or 'haar') through wavedec2() function. This converts images into frequency-domain representations while extracting multi-resolution features from approximation and detail coefficients. Third, PCA is implemented via eigendecomposition of the covariance matrix (using cov() and eig() functions) or singular value decomposition (svd()). This reduces feature dimensionality while preserving the most discriminative facial patterns. The pca() function can automatically select principal components based on variance thresholds. Finally, classifiers like SVM (fitcsvm()) or k-NN (fitcknn()) are trained on the reduced feature set. The classification phase involves feature projection onto the PCA subspace and distance-based matching using techniques such as Euclidean distance or cosine similarity. This integrated approach leverages wavelet decomposition's multi-scale analysis and PCA's dimensionality reduction to significantly enhance recognition accuracy and computational efficiency in automated face identification systems.