Tikhonov’s Regularization to the Deconvolution Problem

Trong, Dang Duc; Phuong, Cao Xuan; Tuyen, Truong Trung; Thanh, Dinh Ngoc

doi:10.1080/03610926.2012.721916

Cited by 7 publications

(3 citation statements)

References 12 publications

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“…However, the inverse problem leading to S V (f ) is unstable due to the noise in the experimental data. To this end, we use Tikhonov regularization [26] to extract the noise density measured by the detector (see [27] for details). It is to be noted that the measured I det,0 [see inset of Fig.…”

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confidence: 99%

Josephson radiation and shot noise of a semiconductor nanowire junction

et al. 2017

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We measured the Josephson radiation emitted by an InSb semiconductor nanowire junction utilizing photon assisted quasiparticle tunneling in an AC-coupled superconducting tunnel junction. We quantify the action of the local microwave environment by evaluating the frequency dependence of the inelastic Cooper-pair tunneling of the nanowire junction and find the zero frequency impedance Z(0) = 492 Ω with a cutoff frequency of f0 = 33.1 GHz. We extract a circuit coupling efficiency of η ≈ 0.1 and a detector quantum efficiency approaching unity in the high frequency limit. In addition to the Josephson radiation, we identify a shot-noise contribution with a Fano factor F ≈ 1, consistently with the presence of single electron states in the nanowire channel.

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confidence: 99%

Josephson radiation and shot noise of a semiconductor nanowire junction

et al. 2017

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“…In a recent work, Belomestny and Goldenshluger (2019) have shown that the Laplace transform can perform deconvolution for general measurement errors. Another approach consists in using Tikhonov regularization for the convolution operator (Carrasco and Florens, 2011;Trong et al, 2014). In the specific case of uniform noise (also called boxcar deconvolution), it is possible to use ad hoc kernel methods (Groeneboom and Jongbloed, 2003;van Es, 2011).…”

Section: Introductionmentioning

confidence: 99%

Uniform Deconvolution for Poisson Point Processes

Bonnet¹,

Lacour²,

Picard³

et al. 2020

Preprint

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We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle and minimax points of view, and provide new lower bounds when the intensity belongs to a Sobolev ball. By developing the Goldenshluger-Lepski methodology in the case of deconvolution for Poisson processes, we propose an optimal data-driven selection of the kernel's bandwidth, and we provide a heuristic framework to calibrate the estimator in practice. Our method is illustrated on the spatial repartition of replication origins along the human genome.

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“…The popularly used prior models are the Tikhonov model [11], the total variation (TV) type model [12], and the Markov random field (MRF) model [13]. The Tikhonov model is based on the L2 norm.…”

Section: Introductionmentioning

confidence: 99%

Multiframe Superresolution of Vehicle License Plates Based on Distribution Estimation Approach

Jin

Zhao

et al. 2016

Journal of Control Science and Engineering

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Low-resolution (LR) license plate images or videos are often captured in the practical applications. In this paper, a distribution estimation based superresolution (SR) algorithm is proposed to reconstruct the license plate image. Different from the previous work, here, the high-resolution (HR) image is estimated via the obtained posterior probability distribution by using the variational Bayesian framework. To regularize the estimated HR image, a feature-specific prior model is proposed by considering the most significant characteristic of license plate images; that is, the target has high contrast with the background. In order to assure the success of the SR reconstruction, the models representing smoothness constraints on images are also used to regularize the estimated HR image with the proposed feature-specific prior model. We show by way of experiments, under challenging blur with size 7 × 7 and zero-mean Gaussian white noise with variances 0.2 and 0.5, respectively, that the proposed method could achieve the peak signal-to-noise ratio (PSNR) of 22.69 dB and the structural similarity (SSIM) of 0.9022 under the noise with variance 0.2 and the PSNR of 19.89 dB and the SSIM of 0.8582 even under the noise with variance 0.5, which are 1.84 dB and 0.04 improvements in comparison with other methods.

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Tikhonov’s Regularization to the Deconvolution Problem

Cited by 7 publications

References 12 publications

Josephson radiation and shot noise of a semiconductor nanowire junction

Josephson radiation and shot noise of a semiconductor nanowire junction

Uniform Deconvolution for Poisson Point Processes

Multiframe Superresolution of Vehicle License Plates Based on Distribution Estimation Approach

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