As the pathological characteristics of living tissue generally correlate with tissue stiffness, techniques such as ultrasound elastography play an important role in the medical field. One issue with elastography is the limited area of measurement. To determine the spatial distribution of elastic moduli, model-based estimation methods have been developed. However, these methods can only be applied to the observable area, and expanding the estimation area remains problematic. This paper introduces a method to estimate the spatial distribution of elastic moduli over the entire elastic body from locally observed deformation patterns. The reconstruction of elasticity from multiple deformation patterns is formulated as a minimization problem based on the sparseness of the gradient of tissue elasticity. Based on simulation experiments investigating the performance of the proposed method, we confirm that spatial variations in elasticity are effectively estimated and the area of elasticity reconstruction is extended.