Osteoporosis, a skeletal disorder resulting from a decrease in bone density, compromises bone strength and increases the susceptibility to fractures. Accurate diagnosis is imperative to identify individuals at risk of future bone fractures. Among the various non-destructive testing methods available, quadratic frequency modulated thermal wave imaging has recently emerged as a preferred choice due to its enhanced depth probing capabilities at lower frequencies compared to its linear counterpart. While this diagnostic approach is valuable, it does not provide direct bone density values. Therefore, a suitable post-processing technique becomes essential for accurate bone density estimation. In this study, an orthogonal kernel-based random projection post-processing technique is applied to the thermal response data to determine bone density. The resulting random projection coefficients are plotted against density, revealing a polynomial relationship that serves as the basis for osteoporosis detection.