  In the problem of compressive phase retrieval, one wants to recover an
approximately $k$-sparse signal $x \in \mathbb{C}^n$, given the magnitudes of
the entries of $\Phi x$, where $\Phi \in \mathbb{C}^{m \times n}$. This problem
has received a fair amount of attention, with sublinear time algorithms
appearing in \cite{cai2014super,pedarsani2014phasecode,yin2015fast}. In this
paper we further investigate the direction of sublinear decoding for real
signals by giving a recovery scheme under the $\ell_2 / \ell_2$ guarantee, with
almost optimal, $\Oh(k \log n )$, number of measurements. Our result
outperforms all previous sublinear-time algorithms in the case of real signals.
Moreover, we give a very simple deterministic scheme that recovers all
$k$-sparse vectors in $\Oh(k^3)$ time, using $4k-1$ measurements.
