1D PCA Image Compression and Decompression

When implementing 1D PCA for image compression and decompression in MATLAB, users can set the number of eigenvalues to observe the compression results. The implementation typically involves reshaping 2D images into 1D vectors as input data for PCA processing. Additionally, the 1D PCA method can handle multidimensional data by converting 2D images into 1D vectors before applying compression and decompression. Key implementation aspects include mean centering, covariance matrix computation using MATLAB's 'cov' function, eigenvalue decomposition via 'eig', and dimensionality reduction through projection onto principal components. Beyond image processing, 1D PCA serves important roles in feature extraction and data dimensionality reduction applications. Therefore, mastering 1D PCA implementation methods and application scenarios holds significant importance for image processing and data analysis tasks. The MATLAB code typically includes functions for visualization of original versus reconstructed images to evaluate compression quality and information retention.