Image Discrete Cosine Transform, Hadamard Transform, and Fourier Transform

In this article, we explore the process of applying Discrete Cosine Transform (DCT), Hadamard Transform (HT), and Fourier Transform (FT) to input images. We compare the frequency domain characteristics of these three transforms and assess the quality of reconstructed images after inverse transformation. To better understand these transforms, we introduce their fundamental principles and application scenarios, including implementation details such as using MATLAB's dct2() for DCT, fwht() for Hadamard transform, and fft2() for Fourier transform with proper zero-padding and normalization techniques. Additionally, we discuss how to select the most suitable transformation method for specific image processing tasks and analyze their respective advantages and limitations in terms of computational efficiency (e.g., DCT's energy compaction property), frequency localization, and reconstruction fidelity. Through this article, you will gain deeper insights into these transforms and their applications in digital image processing, including practical code implementation considerations for frequency domain filtering and compression algorithms.