  This letter proposes a fast implementation of the regularity-constrained
discrete sine transform (R-DST). The original DST \textit{leaks} the lowest
frequency (DC: direct current) components of signals into high frequency (AC:
alternating current) subbands. This property is not desired in many
applications, particularly image processing, since most of the frequency
components in natural images concentrate in DC subband. The characteristic of
filter banks whereby they do not leak DC components into the AC subbands is
called \textit{regularity}. While an R-DST has been proposed, it has no fast
implementation because of the singular value decomposition (SVD) in its
internal algorithm. In contrast, the proposed regularity-constrained fast sine
transform (R-FST) is obtained by just appending a regularity constraint matrix
as a postprocessing of the original DST. When the DST size is $M\times M$
($M=2^\ell$, $\ell\in\mathbb{N}_{\geq 1}$), the regularity constraint matrix is
constructed from only $M/2-1$ rotation matrices with the angles derived from
the output of the DST for the constant-valued signal (i.e., the DC signal).
Since it does not require SVD, the computation is simpler and faster than the
R-DST while keeping all of its beneficial properties. An image processing
example shows that the R-FST has fine frequency selectivity with no DC leakage
and higher coding gain than the original DST. Also, in the case of $M=8$, the
R-FST saved approximately $0.126$ seconds in a 2-D transformation of $512\times
512$ signals compared with the R-DST because of fewer extra operations.
