Hilbert transforms in the Stepanoff space

2D Image Analysis by Generalized Hilbert Transforms in Conformal Space

This work presents a novel rotational invariant quadrature filter approach called the conformal monogenic signal for analyzing i(ntrinsic)1D and i2D local features of any curved 2D signal such as lines, edges, corners and junctions without the use of steering. The conformal monogenic signal contains the monogenic signal as a special case for i1D signals and combines monogenic scale space, phase...

Entropy encoding, Hilbert space, and Karhunen-Loève transforms

Historically, the Karhunen-Loève KL decomposition arose as a tool from the interface of probability theory and information theory see details with references inside the paper . It has served as a powerful tool in a variety of applications, starting with the problem of separating variables in stochastic processes, say, Xt, and processes that arise from statistical noise, for example, from fracti...

Two-dimensional Hilbert Transforms'

A pr 2 00 9 HILBERT TRANSFORMS AND THE CAUCHY INTEGRAL IN EUCLIDEAN SPACE

We generalize the notions of harmonic conjugate functions and Hilbert transforms to higher dimensional euclidean spaces, in the setting of differential forms and the Hodge-Dirac system. These harmonic conjugates are in general far from being unique, but under suitable boundary conditions we prove existence and uniqueness of conjugates. The proof also yields invertibility results for a new class...

Uniform Bounds for the Bilinear Hilbert Transforms

It is shown that the bilinear Hilbert transforms Hα,β(f, g)(x) = p.v. ∫ R f(x− αt)g(x− βt) dt t map Lp1(R) × Lp2(R) → Lp(R) uniformly in the real parameters α, β when 2 < p1, p2 < ∞ and 1 < p = p1p2 p1+p2 < 2. Combining this result with the main result in [9], we deduce that the operators H1,α map L2(R)×L∞(R) → L2(R) uniformly in the real parameter α ∈ [0, 1]. This completes a program initiated...