We propose two algorithms for jointly estimating the power spectrogram and the room transfer functions of a target signal in diffuse noise. These estimates can be used to design a multichannel Wiener filter, and thereby separate a target signal from an unknown direction from diffuse noise. We express a diffuse noise model as a subspace of a matrix linear space, which consists of Hermitian matrices instead of Euclidean vectors. This general framework enables the design of new general algorithms applicable to all specific noise models, instead of multiple specific algorithms each applicable to a single model. The more general proposed algorithms resulted in superior noise suppression performance to our previous algorithms in terms of an output signal-to-noise ratio (SNR).