This thesis investigates how reliable structural information about proteins can be recovered from large-scale but inherently noisy biological data. Positioned at the intersection of statistical physics, machine learning, and structural biology, the work focuses on the reconstruction and denoising of protein contact maps, which describe spatial proximities between amino acid residues and constitute a key intermediate representation for protein structure prediction. The approach starts from evolutionary information contained in multiple sequence alignments of protein families. Residues that are close in three-dimensional space tend to co-evolve, generating statistical dependencies that can be detected using Direct Coupling Analysis (DCA). DCA infers pairwise couplings between sequence positions and produces a score map that can be interpreted as a weighted network of potential residue contacts.