We study the problem of recovering a signal from magnitudes of its wavelet frame coefficients when the analyzing wavelet is real-valued. We show that every real-valued signal can be uniquely recovered, up to global sign, from its multiwavelet frame coefficients
\[
{
|
W
ϕ
i
f
(
α
m
β
n
,
α
m
)
|
:
i
∈
{
1
,
2
,
3
}
,
m
,
n
∈
Z
}
\{\lvert \mathcal {W}_{\phi _i} f(\alpha ^{m}\beta n,\alpha ^{m}) \rvert : i\in \{1,2,3\}, m,n\in \mathbb {Z}\}
\]
for every
α
>
1
,
β
>
0
\alpha >1,\beta >0
with
β
ln
(
α
)
≤
4
π
/
(
1
+
4
p
)
\beta \ln (\alpha )\leq 4\pi /(1+4p)
,
p
>
0
p>0
, when the three wavelets
ϕ
i
\phi _i
are suitable linear combinations of the Poisson wavelet
P
p
P_p
of order
p
p
and its Hilbert transform
H
P
p
\mathscr {H}P_p
. For complex-valued signals we find that this is not possible for any choice of the parameters
α
>
1
,
β
>
0
\alpha >1,\beta >0
, and for any window. In contrast to the existing literature on wavelet sign retrieval, our uniqueness results do not require any bandlimiting constraints or other a priori knowledge on the real-valued signals to guarantee their unique recovery from the absolute values of their wavelet coefficients.