Accurate reconstruction of full-field structural responses from sparse measurements remains a central challenge in inverse structural mechanics, particularly when sensing configurations are severely limited or unbalanced [1,2]. In plate shape sensing, classical displacement recovery methods (e.g., inverse FEM formulations) typically require dense and well-distributed measurements and often rely on back-to-back strain sensing to reconstruct accurate full fields [3]. However, under single-sided sensing and sparse instrumentation, the inverse mapping becomes ill-conditioned, highly non-unique, and strongly sensitive to measurement noise and modeling errors. These limitations make reliable full-field recovery difficult to achieve without substantial sensor coverage or computationally intensive forward analyses. This work presents a mixed-measurement inverse reconstruction strategy for Mindlin plates within an Inverse Spectral Chebyshev–Compressed Sensing (ISC–CS) framework. The method exploits spectral compressibility to reconstruct a dense strain field in Chebyshev coefficient space from sparse strain observations via an enhanced sparse-recovery solver, while a small number of displacement measurements is enforced as constraints on low-order spectral coefficients to regularize weakly identifiable components under extreme sparsity. The resulting dense strain field is then coupled with kinematic relations to recover displacements and rotations without requiring prior knowledge of the applied loads. The mixed formulation naturally resolves the dominant spectral content of the displacement field while exposing a small set of weakly constrained low-order spectral components in strain-only settings. Introducing a very small number of displacement measurements constrains these low-order components and substantially improves reconstruction robustness under severe data sparsity. Beyond improved accuracy with minimal additional instrumentation, the approach provides a spectral interpretation of why dense-but-inexact reconstructed strain fields can still yield high-fidelity displacement fields when complemented by a handful of displacement anchors, establishing a practical sensing and inversion paradigm for full-field shape sensing in data-limited scenarios.