  We propose a new algorithm for joint dereverberation and blind source
separation (DR-BSS). Our work builds upon the IRLMA-T framework that applies a
unified filter combining dereverberation and separation. One drawback of this
framework is that it requires several matrix inversions, an operation
inherently costly and with potential stability issues. We leverage the recently
introduced iterative source steering (ISS) updates to propose two algorithms
mitigating this issue. Albeit derived from first principles, the first
algorithm turns out to be a natural combination of weighted prediction error
(WPE) dereverberation and ISS-based BSS, applied alternatingly. In this case,
we manage to reduce the number of matrix inversion to only one per iteration
and source. The second algorithm updates the ILRMA-T matrix using only
sequential ISS updates requiring no matrix inversion at all. Its implementation
is straightforward and memory efficient. Numerical experiments demonstrate that
both methods achieve the same final performance as ILRMA-T in terms of several
relevant objective metrics. In the important case of two sources, the number of
iterations required is also similar.
