Analisis Komparatif Representasi Frekuensi dan Kualitas Rekonstruksi Citra Digital Menggunakan Algoritma FFT dan DWT Haar

Abstract

Image processing in the spatial domain has limitations in computation and detailed analysis, so transformation to the frequency domain is a solution. This study aims to compare the Haar Fast Fourier Transform (FFT) and Discrete Wavelet Transform (DWT) methods on the frequency representation and quality of digital image reconstruction. The test was conducted using the Python programming language on Cameraman and Lena grayscale images with dimensions of 256x256 pixels. The quality of the reconstruction image was evaluated quantitatively using the Mean Square Error (MSE) and Peak Signal to Noise Ratio (PSNR) parameters. Visual results show that FFT effectively concentrates intensity globally on the DC Coefficient but loses spatial information, whereas DWT Haar is able to maintain its original spatial structure in the Approximation sub-band. At the reconstruction stage, both methods were proven to reconstruct the image perfectly (lossless) with an MSE error of 0.0000. The FFT method yielded a PSNR value of 324.14 dB, slightly higher than the DWT of 316.22 dB. In conclusion, although FFT has a slight advantage quantitatively, DWT Haar is considered more adaptive and functional for modern image processing applications such as compression and noise reduction due to its ability to localize object details.