For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L(R), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions which are smooth away from singularities along k-planes in R. We also develop tools to help decide whether in fact k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tigh...

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L (R), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions which are smooth away from singularities along k-planes in R. We also develop tools to help decide whether in fact k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tig...

The theory of frames is fundamental to timefrequency (TF or time-scale signal expansions like Gabor ysis of frames via two “TF frame representations” called the Weyl symbol and Wigner distribution of a frame. The T F analysis shows how a frame’s properties depend on the signal’s T F location and on certain frame parameters. 1 I N T R O D U C T I O N Linear time-frequency (TF) or time-scale sign...

Under certain assumptions we show that a wavelet frame {τ(Aj , bj,k)ψ}j,k∈Z := {|detAj |−1/2ψ(A−1 j (x− bj,k))}j,k∈Z in L2(Rd) remains a frame when the dilation matrices Aj and the translation parameters bj,k are perturbed. As a special case of our result, we obtain that if {τ(Aj , ABn)ψ}j∈Z,n∈Zd is a frame for an expansive matrix A and an invertible matrix B, then {τ(Aj , ABλn)ψ}j∈Z,n∈Zd is a ...

If the wavelet system {aψ(a ·−bk)}j,k∈Z forms a frame onL(R) for some a > 1 and b > 0, then it is called a (regular) wavelet frame. In this case we can reconstruct any f from the sampled values (Wψf)(a , abk). In practice the sampling points may be irregular. We need to know for which wavelet ψ and parameters {(sj , bk)}j,k , the wavelet system {s j ψ(sj · −bk)}j,k∈Z forms a frame on L (R). In ...

We give lower frame bounds for finite subfamilies of a frame of exponentials {ek}k∈Z in L2(−π, π). We also present a method for approximation of the inverse frame operator corresponding to {ek}k∈Z, where knowledge of the frame bounds for finite subfamilies is crucial.

For each pair (n, k) with 1 </= k < n, we construct a tight frame (rholambda : lambda in Lambda) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wa...