Deconvolution model with fractional Gaussian noise: A minimax study

Benhaddou, Rida

doi:10.1016/j.spl.2016.05.022

Cited by 9 publications

(12 citation statements)

References 8 publications

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“…The following theorem shows that, when initialized with the LS estimator (8), these iterations converge to a limit with a simple explicit form. The result described in (16) below is our proposed estimator.…”

Section: "Self-wiener" Filteringmentioning

confidence: 99%

“…An equivalent, yet different enlightening expression for the SW estimator ( 16) is given as follows. Focusing on the case |Z[k]| > 2, by multiplying the numerator and denominator in (16)…”

Section: "Self-wiener" Filteringmentioning

confidence: 99%

“…We now provide some intuition for our proposed estimator, (16). Note that the unrealizable optimal solution (11) is the LS estimator multiplied by a regularization term, which depends on the unknown X[k].…”

Section: "Self-wiener" Filteringmentioning

confidence: 99%

“…While the random signal model is suitable in some problems and scenarios, in others the input signal is better modeled as deterministic unknown. Several methods have been proposed for this signal model as well [14]- [16]. One example is the WaveD algorithm proposed by Johnstone et al [17], which is based on hard thresholding of a wavelet expansion (see also [18], Section II, for a concise description of WaveD).…”

Section: Introductionmentioning

confidence: 99%

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"Self-Wiener" Filtering: Data-Driven Deconvolution of Deterministic Signals

Weiss¹,

Nadler²

2020

Preprint

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We consider the fundamental problem of robust deconvolution, and particularly the recovery of an unknown deterministic signal convolved with a known filter and corrupted by additive noise. We present a novel, non-iterative data-driven approach. Specifically, our algorithm works in the frequencydomain, where it tries to mimic the optimal unrealizable Wienerlike filter as if the unknown deterministic signal were known. This leads to a threshold-type regularized estimator, where the threshold value at each frequency is found in a fully datadriven manner. We provide an analytical performance analysis, and derive approximate closed-form expressions for the residual Mean Squared Error (MSE) of our proposed estimator in the low and high Signal-to-Noise Ratio (SNR) regimes. We show analytically that in the low SNR regime our method provides enhanced noise suppression, and in the high SNR regime it approaches the performance of the optimal unrealizable solution. Further, as we demonstrate in simulations, our solution is highly suitable for (approximately) bandlimited or frequency-domain sparse signals, and provides a significant gain of several dBs relative to other methods in the resulting MSE.

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Section: "Self-wiener" Filteringmentioning

confidence: 99%

“…An equivalent, yet different enlightening expression for the SW estimator ( 16) is given as follows. Focusing on the case |Z[k]| > 2, by multiplying the numerator and denominator in (16)…”

Section: "Self-wiener" Filteringmentioning

confidence: 99%

Section: "Self-wiener" Filteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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"Self-Wiener" Filtering: Data-Driven Deconvolution of Deterministic Signals

Weiss¹,

Nadler²

2020

Preprint

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“…Lemma 1 Let U ω be defined in (7), and let h 1 and h 2 satisfy (10). Then, under condition (9) and provided that s 10 > max{ν, r}, one has…”

Section: Estimation Algorithmmentioning

confidence: 99%

Anisotropic Functional Deconvolution for the irregular design with dependent long-memory errors

Benhaddou

2019

Preprint

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Anisotropic functional deconvolution model is investigated in the bivariate case under long-memory errors when the design points tirregular and follow known densities h 1 , h 2 , respectively. In particular, we focus on the case when the densities h 1 and h 2 have singularities, but 1/h 1 and 1/h 2 are still integrable on [0, 1].Under both Gaussian and sub-Gaussian errors, we construct an adaptive wavelet estimator that attains asymptotically near-optimal convergence rates that deteriorate as long-memory strengthens. The convergence rates are completely new and depend on a balance between the smoothness and the spatial homogeneity of the unknown function f , the degree of ill-posedness of the convolution operator, the long-memory parameter in addition to the degrees of spatial irregularity associated with h 1 and h 2 . Nevertheless, the spatial irregularity affects convergence rates only when f is spatially inhomogeneous in either direction.

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Deconvolution model with fractional Gaussian noise: A minimax study

Cited by 9 publications

References 8 publications

"Self-Wiener" Filtering: Data-Driven Deconvolution of Deterministic Signals

"Self-Wiener" Filtering: Data-Driven Deconvolution of Deterministic Signals

Anisotropic Functional Deconvolution for the irregular design with dependent long-memory errors

Minimax lower bounds for the simultaneous wavelet deconvolution with fractional Gaussian noise and unknown kernels

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