Fourier Reconstruction

This paper presents Fourier reconstruction as a method for recovering original images. The technique relies on Fourier transforms to convert signals into the frequency domain for analysis. Through inverse transformation, the signal can be reconstructed back to the spatial domain, yielding an approximation of the original signal. Typically implemented using Fast Fourier Transform (FFT) algorithms like numpy.fft.fft2() for 2D images, the process involves three key computational stages: frequency domain conversion via FFT, frequency component modification (filtering/denoising), and spatial domain reconstruction using inverse FFT (numpy.fft.ifft2()). This methodology finds extensive application in image and signal processing as it enables fundamental frequency-domain interpretation of visual data, particularly useful in medical imaging (CT/MRI) and astronomical image restoration where it helps eliminate noise while preserving critical structural information through selective frequency component manipulation.