Tomographic Reconstruction Via Fourier And Wavelet Transformations: Enhancing Signal Analysis Techniques

Abstract

Tomographic reconstruction is essential in medical and industrial imaging, which reconstructs cross-sectional structures from projection data. Conventional reconstruction algorithms, primarily relying on Fourier transforms, effectively reconstruct global frequency patterns, but may introduce artifacts in the case of low-dose or limited-angle CT. The wavelet transformations are useful for the preservation of the localized details but fail in coherency in broader structures and are noisy in smooth areas. In this work, a new Fourier-wavelet model is proposed as the integration of the Fourier and wavelet transformations that provide high-quality tomographic reconstructions. The hybrid approach of Fourier’s global frequency capture with wavelet’s spatial localization reduces artifacts, improves edge preservation, and optimizes structural preservation, especially in situations with limited projection. Numerical analysis shows that the hybrid model is 40% more accurate in reconstruction error than Fourier-only and 30% more accurate than wavelet-only methods. This model offers a feasible and efficient solution for image reconstruction in the low-data and noisy environment and can be used in the low-dose CT and industrial imaging. These results evidence the effectiveness of the hybrid approach to offer artifact-minimal reconstructions, which is a major advancement toward enhancing the accuracy and time efficiency of tomographic imaging.