A hearing device comprising • an input unit for delivering a time varying electric input signal (x; x(t n); x 1,..., x M) representing an audio signal comprising at least two sound sources (S 1, S 2; S 1, S N), • a sound source separation unit for separating said electric input signal (x; x(t n); x 1,..., x M) to provide at least two separated signals (s 1, s 2; s 1,..., s N) representing said at least two sound sources (S 1, S 2; S 1,..., S N), CHARACTERIZED IN THAT the hearing device further comprises • a cyclic analysis buffer unit (A-BUF) of length A adapted for storing the last A audio samples, and • a cyclic synthesis buffer unit (S-BUF) of length L, where L is smaller than A, adapted for storing the last L audio samples, which are intended to be separated in individual sound sources, • a database (DATABASE) having stored recorded sound examples d k n from said at least two sound sources (S 1, S 2; S 1,..., S N), each recorded sound example in the database being termed an atom, where n is a sound source index, and k is an atom index, the atoms originating from audio samples from first and second buffers corresponding in size to said synthesis (S-BUF) and said analysis (A-BUF) buffer units, respectively, where for each atom, the audio samples from the first buffer overlap with the audio samples from the second buffer, and where atoms originating from the first buffer constitute a reconstruction dictionary ( R 1, R 2), and where atoms originating from the second buffer constitute an analysis dictionary ( A 1, A 2), and wherein • the sound source separation unit is configured to determine the most optimal representation of the last A audio samples given the atoms in the analysis dictionary ( A 1, A 2) of the database (DATABASE), and to generate said at least two separated signals (s 1, s 2; s 1,.... s N) of L audio samples by combining atoms in the reconstruction dictionary ( R 1, R 2) of the database using the optimal representation. • an input unit for delivering a time varying electric input signal (x; x(t n); x 1,..., x M) representing an audio signal comprising at least two sound sources (S 1, S 2; S 1, S N), • a sound source separation unit for separating said electric input signal (x; x(t n); x 1,..., x M) to provide at least two separated signals (s 1, s 2; s 1,..., s N) representing said at least two sound sources (S 1, S 2; S 1,..., S N), CHARACTERIZED IN THAT the hearing device further comprises • a cyclic analysis buffer unit (A-BUF) of length A adapted for storing the last A audio samples, and • a cyclic synthesis buffer unit (S-BUF) of length L, where L is smaller than A, adapted for storing the last L audio samples, which are intended to be separated in individual sound sources, • a database (DATABASE) having stored recorded sound examples d k n from said at least two sound sources (S 1, S 2; S 1,..., S N), each recorded sound example in the database being termed an atom, where n is a sound source index, and k is an atom index, the atoms originating from audio samples from first and second buffers corresponding in size to said synthesis (S-BUF) and said analysis (A-BUF) buffer units, respectively, where for each atom, the audio samples from the first buffer overlap with the audio samples from the second buffer, and where atoms originating from the first buffer constitute a reconstruction dictionary ( R 1, R 2), and where atoms originating from the second buffer constitute an analysis dictionary ( A 1, A 2), and wherein • the sound source separation unit is configured to determine the most optimal representation of the last A audio samples given the atoms in the analysis dictionary ( A 1, A 2) of the database (DATABASE), and to generate said at least two separated signals (s 1, s 2; s 1,.... s N) of L audio samples by combining atoms in the reconstruction dictionary ( R 1, R 2) of the database using the optimal representation.