The gradient method, Levenberg-Marquardt (LM) method, L₂ cooled roughness (CRL2) method and L₁ cooled roughness (CRL1) method are applied to the problem of recovering the relative permittivity structure of a dielectric object. The CRL1 method is a novel technique for the recovery of the relative permittivity structure of a dielectric object introduced in this work. The frequencies used in this work range from 0.80Hz to 1.2 GHz. The size of the permittivity structure is approximately 1 wavelength, which is approximately 30cm at 10Hz. The gradient method and LM method were unable to recover the relative permittivity structure unless the starting model is very close to the target. Both methods require a starting model that is close to the target model for them to be successful. The CRL2 method was able to recover a blurry approximation to the target relative permittivity structure. The blurriness is due to the L₂ norm. The CRL1 method is able to recover “blocky” structure. In the absence of noise, the CRL1 method was able to recover structure that was approximately one third wavelength in size. The recovery of structure at a fraction of a wavelength is highly sensitive to noise. Even at 0.0 1% noise, the CRL1 algorithm had difficulty recovering the exact structure.