Learning multiplication-free linear transformations

In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such they have low coding complexity and are numerically efficient to use: reduced number of addition/multiplications even avoid multiplications altogether. We base our work factorizations in highly structured basic building blocks (binary orthonormal, scaling, shear transformations) which can write closed-form solutions optimization problems consider. show effectiveness methods image data where compare against well-known transforms as fast Fourier, discrete cosine transforms, dictionaries.