Elastography is a key technique for non-invasive imaging, yet it remains severely ill-posed and sensitive to measurement noise, causing blurring and artifacts. We propose EL-DIP, a training-data-free framework based on deep image prior (DIP) that reconstructs heterogeneous shear modulus distributions. Inverse distance weighting interpolation enables arbitrary-shaped domains, and adjoint sensitivity analysis provides efficient gradient computation. Numerical and experimental studies show that EL-DIP accurately recovers inclusion geometry and modulus across different noise levels. Under extreme noise, image fidelity improves by approximately 97.1% over conventional methods. We believe that this method has great potential as a robust tool for biomedical diagnosis,biomechanical characterization, and non-destructive evaluation.

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