Goldstein Filtering Method: MATLAB Implementation for ESPI, InSAR, and Fingerprint Image Processing

This article presents a MATLAB implementation of the Goldstein filtering method, which can be applied to ESPI electronic speckle patterns, InSAR fringe patterns, and fingerprint image filtering. The Goldstein filter is a widely-used signal processing algorithm that operates by processing input signals to extract useful information while removing noise interference, thereby producing clearer and more accurate results. In MATLAB implementation, the algorithm typically involves transforming the input image to the frequency domain using FFT (Fast Fourier Transform), applying adaptive filtering based on local frequency characteristics, and reconstructing the filtered image through inverse FFT. Key parameters include filter window size, compression factor, and iteration controls that determine noise suppression strength and feature preservation. For ESPI electronic speckle patterns, the Goldstein filtering method processes speckle images to enhance pattern visibility by reducing random speckle noise while maintaining phase information critical for displacement measurements. The implementation requires careful parameter tuning to balance noise reduction and signal preservation. In InSAR fringe patterns, Goldstein filtering effectively removes noise from interferometric fringes, resulting in smoother and clearer fringe patterns that facilitate more accurate phase unwrapping and deformation analysis. The algorithm's adaptive nature allows it to preserve fringe edges while suppressing background noise. For fingerprint images, the Goldstein method extracts ridge characteristics by filtering out noise interference, producing clearer and more reliable fingerprint images for biometric applications. The implementation typically includes preprocessing steps like contrast enhancement followed by frequency-domain filtering to emphasize ridge-valley patterns. The MATLAB code structure generally consists of image input modules, frequency transformation functions, adaptive filtering kernels with Goldstein's weighting coefficients, and image reconstruction routines. Proper implementation requires handling boundary conditions and optimizing computational efficiency for large datasets.