Blind source separation (BSS) consists in estimating a set of unknown sources from a set of observations resulting from mixtures of these sources through unknown propagation channels. For that purpose, methods usually assume the sources to be statistically independent, non-negative and/or sparse. A signal is said to be sparse in a representation domain if most of its atoms are zero or close to zero. Most of sparsity-based BSS methods require the disjointness of the sources in the representation domain: in each atom, they assume that one and only one source is non-zero. On the contrary, a few approaches, including those I developed, require highly relaxed sparsity assumptions, hence their name of Quasi-Non-Sparse Component Analysis. In this presentation, I will briefly introduce such methods for linear instantaneous, anechoic, and convolutive mixtures and I will illustrate their performance with audio and astrophysical applications.