This paper presents a novel approach to estimate the \(\mu\) and y-distortions in the Cosmic Microwave Background (CMB) using the COBE/FIRAS data. The analysis draws from the concept of blackbody radiation inversion (BRI), a mathematical technique typically used to determine the temperature distribution from a radiated power spectrum. We study the deviations from the ideal blackbody spectrum or the spectral distortions by incorporating first a non-zero chemical potential \(\mu\) via the Bose-Einstein distribution and then also adding the Compton parameter y while keeping the monopole temperature constant. We infer the results as probability distribution functions on these distortions. Finally, we derive \(\mu = {(-\,0.656 \;\pm \; 2.048) \times 10^{-5}}\) and \(y = {5.498 \times 10^{-10} \pm 2.775 \times 10^{-6}}\) at a \(68\%\) confidence interval. Here we show how the BRI method performs in a test-case scenario, illustrating its potential for extracting spectral distortion parameters in CMB.
