Complex sentence: Hence, shearlets provide "optimally sparse approximations" of cartoon-like images, whereas the achievable rates for wavelet and Fourier systems are far from optimal, namely O (N ^) and O (N ^) respectively.
Split into simpler sentences: Hence, shearlets provide "optimally sparse approximations" of cartoon-like images. However, the achievable rates for wavelet and Fourier systems are far from optimal, namely O (N ^) and O (N ^) respectively.