  Low-rank matrix approximation plays an increasingly important role in signal
and image processing applications. This paper presents a new rank-revealing
decomposition method called randomized rank-revealing UZV decomposition
(RRR-UZVD). RRR-UZVD is powered by randomization to approximate a low-rank
input matrix. Given a large and dense matrix ${\bf A} \in \mathbb R^{m \times
n}$ whose numerical rank is $k$, where $k$ is much smaller than $m$ and $n$,
RRR-UZVD constructs an approximation $\hat{\bf A}$ such as $\hat{\bf A}={\bf
UZV}^T$, where ${\bf U}$ and ${\bf V}$ have orthonormal columns, the
leading-diagonal block of ${\bf Z}$ reveals the rank of $\bf A$, and its
off-diagonal blocks have small $\ell_2$-norms. RRR-UZVD is simple, accurate,
and only requires a few passes through $\bf A$ with an arithmetic cost of
$O(mnk)$ floating-point operations. To demonstrate the effectiveness of the
proposed method, we conduct experiments on synthetic data, as well as real data
in applications of image reconstruction and robust principal component
analysis.
