We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...

The present paper for the first time 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...

Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides (optimally) sparse approximations of the original image. Due to the common assumption that images are typically governed by anisotropic features, directional represen...