Learning Explicitly Conditioned Sparsifying Transforms
This work addresses a specific issue in signal processing for researchers and practitioners, offering an incremental improvement over existing transform learning methods.
The paper tackles the problem of learning sparsifying transforms by proposing a new model that explicitly controls data representation quality and condition number, showing through experiments that it outperforms state-of-the-art methods with better numerical behavior.
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.