  The Karhunen-Lo\`eve transform (KLT) is often used for data decorrelation and
dimensionality reduction. Because its computation depends on the matrix of
covariances of the input signal, the use of the KLT in real-time applications
is severely constrained by the difficulty in developing fast algorithms to
implement it. In this context, this paper proposes a new class of
low-complexity transforms that are obtained through the application of the
round function to the elements of the KLT matrix. The proposed transforms are
evaluated considering figures of merit that measure the coding power and
distance of the proposed approximations to the exact KLT and are also explored
in image compression experiments. Fast algorithms are introduced for the
proposed approximate transforms. It was shown that the proposed transforms
perform well in image compression and require a low implementation cost.
