Decomposing Images into High-Frequency and Low-Frequency Components

Using MATLAB to decompose images into high-frequency and low-frequency components. First, we can apply Fourier Transform (using fft2 function) to convert the image into frequency domain representation. Then, by designing appropriate frequency filters (such as low-pass and high-pass filters), we separate the high-frequency and low-frequency components. Common implementation approaches include using Gaussian filters or ideal frequency domain filters with specified cutoff frequencies. The low-frequency component typically represents the overall structure and gradual color transitions, while the high-frequency component captures fine details and edges. Next, we apply Inverse Fourier Transform (ifft2 function) to reconstruct both components separately in the spatial domain. Finally, we display the reconstructed high-frequency and low-frequency components using MATLAB's visualization functions (imshow or imagesc) to better understand the frequency characteristics of the image. This decomposition process helps in analyzing image features and is fundamental for applications like image enhancement, compression, and noise reduction.