A hearing aid includes an input providing an input signal representing sound in an environment, the input signal including no speech signal, or one or more speech signals from one or more speech sound sources and additional signal components, termed noise signal, from one or more other sound sources, an own voice detector, a voice activity detector, and a talker extraction unit to determine and/or receive one or more speech signals as separated one or more speech signals from speech sound sources other than the hearing aid user and to detect the speech signal originating from the voice of the user. The talker extraction unit provides separate signals, each including, or indicating presence of, one of the one or more speech signals. A noise reduction system determines speech overlap and/or gap between the speech signal originating from the user's voice and each of the separated one or more speech signals.