  Sparsifying transforms became in the last decades widely known tools for
finding structured sparse representations of signals in certain transform
domains. Despite the popularity of classical transforms such as DCT and
Wavelet, learning optimal transforms that guarantee good representations of
data into the sparse domain has been recently analyzed in a series of papers.
Typically, the conditioning number and representation ability are complementary
key features of learning square transforms that may not be explicitly
controlled in a given optimization model. Unlike the existing approaches from
the literature, in our paper, we consider a new sparsifying transform model
that enforces explicit control over the data representation quality and the
condition number of the learned transforms. We confirm through numerical
experiments that our model presents better numerical behavior than the
state-of-the-art.
