MR elastography (MRE) is a phase-contrast MR technique in which the shear stiffness of soft tissues can be estimated. Helmholtz equation-based inversion is used to obtain stiffness of interest from MRE measurements. It is challenging to accurately estimate stiffness due to the presence of noise. In this work, an inversion method based on unconstrained optimization has been proposed where noise is reduced from the measured data while the sparsity of stiffness map in wavelet domain is being explored. Results demonstrated that optimization yielded more accurate stiffness estimation with lower root-mean-square error and lower maximum error when compared to local-frequency estimation.