Higher-rank wavelet transforms, ridgelet transforms, and Radon transforms on the space of matrices
نویسندگان
چکیده
منابع مشابه
Multiscaled Wavelet Transforms, Ridgelet Transforms, and Radon Transforms on the Space of Matrices
Let Mn,m be the space of real n × m matrices which can be identified with the Euclidean space R. We introduce continuous wavelet transforms on Mn,m with a multivalued scaling parameter represented by a positive definite symmetric matrix. These transforms agree with the polar decomposition on Mn,m and coincide with classical ones in the rank-one case m = 1. We prove an analog of Calderón’s repro...
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Images are typically described via orthogonal, non-redundant transforms like wavelet or discrete cosine transform. The good performances of wavelets in one-dimensional domain are lost when they are applied to images using 2D separable basis since they are not able to efficiently code one-dimensional singularities. The Ridgelet transform achieves very compact representation of linear singulariti...
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We develop an analytic approach to the Radon transform f̂(ζ) = ∫ τ⊂ζ f(τ), where f(τ) is a function on the affine Grassmann manifold G(n, k) of k-dimensional planes in Rn, and ζ is a k′-dimensional plane in the similar manifold G(n, k′), k′ > k. For f ∈ Lp(G(n, k)), we prove that this transform is finite almost everywhere on G(n, k′) if and only if 1 ≤ p < (n− k)/(k′− k), and obtain explicit inv...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2006
ISSN: 1063-5203
DOI: 10.1016/j.acha.2006.01.002