Wavelets have found widespread applications in modern signal processing, image analysis, and noise reduction. However, their use in quantum field theories has remained largely unexplored. At the same time, lattice QCD calculations, particularly those involving nuclei, are often limited by severe signal-to-noise degradation in correlation functions. We introduce a novel quark-smearing method based on wavelets that efficiently projects quark fields onto a low-energy subspace. This approach is used to construct sparse estimators of multi-hadron correlation functions. We demonstrate that the ground-state signals obtained with the wavelet-based method are consistent with those from the full correlation functions while reducing the computational cost substantially. Furthermore, we incorporate wavelet basis functions into both exact and stochastic distillation frameworks. The resulting formulation enables efficient computation of single- and multi-hadron and momentum correlation functions with significantly reduced Wick-contraction costs and memory requirements, without compromising the quality of the extracted signals. In this talk, I will present the wavelet-based formulation, its implementation within the distillation framework, and discuss its broader applications to lattice field theories.
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