Digital Image Processing: Filtering and Fourier Compression

In digital image processing, filtering and Fourier compression are fundamental concepts. Filtering techniques involve applying various types of filters to modify image characteristics. This article examines several common filters: Ideal Low-Pass Filter (eliminates high-frequency components above a cutoff frequency), Butterworth High-Pass Filter (provides smoother frequency response with adjustable order parameter), Gaussian Band-Pass Filter (selects specific frequency ranges using Gaussian distribution), and Gaussian Band-Stop Filter (suppresses particular frequency bands). Additionally, we explore FFT image compression, which utilizes Fast Fourier Transform to reduce image file size by eliminating less significant frequency components. Code implementations typically involve frequency domain transformations using fft2() in MATLAB or np.fft.fft2() in Python, followed by frequency component manipulation and inverse transformation. Comparative screenshots of original and processed images demonstrate practical applications. Through this study, readers will gain comprehensive understanding of filtering principles and Fourier compression mechanisms in digital image processing.