Separation of CMB $\mu$ spectral distortions from foregrounds with poorly defined spectral shapes

This paper proposes a new approach to separate the $\mu$ spectral distortions of the cosmic microwave background from foregrounds with poorly defined spectral shapes. The idea is based on finding the optimal response to the observed signal. This response is weakly sensitive to foregrounds with parameters that are within some certain limits of their possible variations and, at the same time, very sensitive to the amplitude of $\mu$ distortion. The algorithm described in this paper is stable, easy to implement, and simultaneously minimizes the response to foregrounds and photon noise.