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QOL (quality of life) in old age has received much attention. Fracture of bones is seriously related to the QOL and is mainly caused by osteoporosis in old age. BMD (bone mineral density), an index to evaluate the mechanical strength of the bone, does not always reflect the strength. On the other hand, micro X-ray CT has revealed the inner structure of bone. Under such circumstances, an image compression technique was employed to find a better index for the evaluation. MRA (multi resolution analysis) and a measure for the subband images are popular techniques. In this study, the MRA with Harr functions and the power spectra of the subband images were employed. A linear estimation with the power spectra was performed to estimate the strength. To evaluate this method, the micro X-ray CT imaging and a destructive test of rat lumbar vertebras were performed. The newly determined index was higher correlated to the bone mechanical strength than the BMD. The situation for human bone may not be so different from the rat bones. This method may be, therefore, beneficial to estimating the bone mechanical strength in humans.