Adaptive wavelet methods for elliptic operator equations: convergence rates
Mathematics of Computation
Adaptive Solution of Operator Equations Using Wavelet Frames
SIAM Journal on Numerical Analysis
Full length article: Compactly supported shearlets are optimally sparse
Journal of Approximation Theory
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
The contourlet transform: an efficient directional multiresolution image representation
IEEE Transactions on Image Processing
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The present paper constructs a frame/dual frame pair of shearlet type such that both frames possess the distinctive time-frequency localization properties needed in establishing their desirable approximation properties. Our construction is based on a careful pasting together of two bandlimited shearlet Parseval frames associated with two different frequency cones, inspired by domain decomposition methods used primarily for the solution of PDEs.