Cone-Beam Computed Tomography (CBCT) is essential in medical imaging, and the Feldkamp-Davis-Kress (FDK) algorithm is a popular choice for reconstruction due to its efficiency. However, FDK is susceptible to noise and artifacts. While recent deep learning methods offer improved image quality, they often increase computational complexity and lack the interpretability of traditional methods. In this paper, we introduce an enhanced FDK-based neural network that maintains the classical algorithm's interpretability by selectively integrating trainable elements into the cosine weighting and filtering stages. Recognizing the challenge of a large parameter space inherent in 3D CBCT data, we leverage wavelet transformations to create sparse representations of the cosine weights and filters. This strategic sparsification reduces the parameter count by $93.75\%$ without compromising performance, accelerates convergence, and importantly, maintains the inference computational cost equivalent to the classical FDK algorithm. Our method not only ensures volumetric consistency and boosts robustness to noise, but is also designed for straightforward integration into existing CT reconstruction pipelines. This presents a pragmatic enhancement that can benefit clinical applications, particularly in environments with computational limitations.