  In this paper, a new signal processing framework is proposed, in which the
array time samples are represented in DOA-frequency domain through a single
stage problem. It is shown that concatenated array data is well represented in
a $\mathbf{G}$ dictionary atoms space, where $\mathbf{G}$ columns correspond to
pixels in the DOA-frequency image. We present two approaches for the
$\mathbf{G}$ formation and compare the benefits and disadvantages of them. A
mutual coherence guaranteed $\mathbf{G}$ manipulation technique is also
proposed. Furthermore, unlike most of the existing methods, the proposed
problem is reversible into the time domain, therefore, source recovery from the
resulted DOA-frequency image is possible. The proposed representation in
DOA-frequency domain can be simply transformed into a group sparse problem, in
the case of non-multitone sources in a given bandwidth. Therefore, it can also
be utilized as an effective wideband DOA estimator. In the simulation part, two
scenarios of multitone sources with unknown frequency and DOA locations and
non-multitone wideband sources with assumed frequency region are examined. In
multitone scenario, sparse solvers yield more accurate DOA-frequency
representation compared to some noncoherent approaches. At the latter scenario,
the proposed method with group sparse solver outperforms some existing wideband
DOA estimators in low SNR regime. In addition, sources' recovery simultaneous
with DOA estimation shows significant improvement compared to the conventional
delay and sum beamformer and without prerequisites required in sophisticated
wideband beamformers.
