Image Denoising

Elad, Michael

doi:10.1007/978-1-4419-7011-4_14

Cited by 5 publications

(3 citation statements)

References 47 publications

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“…The least absolute shrinkage and selection operator (LASSO) [ 21 ] is such regression model. However, over the last decade a number of methods for sparse solution of the linear inverse problems with the formulations equivalent to above, have been developed [ 22 – 24 ] and conditions necessary for uniqueness of the solution are established. To be more specific, let us suppose that k = | w | 0 , i.e.…”

Section: Resultsmentioning

confidence: 99%

Predicting Antitumor Activity of Peptides by Consensus of Regression Models Trained on a Small Data Sample

Radman

Gredičak

Kopriva

et al. 2011

IJMS

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Predicting antitumor activity of compounds using regression models trained on a small number of compounds with measured biological activity is an ill-posed inverse problem. Yet, it occurs very often within the academic community. To counteract, up to some extent, overfitting problems caused by a small training data, we propose to use consensus of six regression models for prediction of biological activity of virtual library of compounds. The QSAR descriptors of 22 compounds related to the opioid growth factor (OGF, Tyr-Gly-Gly-Phe-Met) with known antitumor activity were used to train regression models: the feed-forward artificial neural network, the k-nearest neighbor, sparseness constrained linear regression, the linear and nonlinear (with polynomial and Gaussian kernel) support vector machine. Regression models were applied on a virtual library of 429 compounds that resulted in six lists with candidate compounds ranked by predicted antitumor activity. The highly ranked candidate compounds were synthesized, characterized and tested for an antiproliferative activity. Some of prepared peptides showed more pronounced activity compared with the native OGF; however, they were less active than highly ranked compounds selected previously by the radial basis function support vector machine (RBF SVM) regression model. The ill-posedness of the related inverse problem causes unstable behavior of trained regression models on test data. These results point to high complexity of prediction based on the regression models trained on a small data sample.

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Section: Resultsmentioning

confidence: 99%

Predicting Antitumor Activity of Peptides by Consensus of Regression Models Trained on a Small Data Sample

Radman

Gredičak

Kopriva

et al. 2011

IJMS

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“…Given that a dictionary D has a coherence µ, it is known that the RIP constant can be upper bounded by µ in the following way [22] …”

Section: Incoherent Dictionariesmentioning

confidence: 99%

Greedy signal space methods for incoherence and beyond

Giryes

Needell

2015

Applied and Computational Harmonic Analysis

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ABSTRACT. Compressive sampling (CoSa) has provided many methods for signal recovery of signals compressible with respect to an orthonormal basis. However, modern applications have sparked the emergence of approaches for signals not sparse in an orthonormal basis but in some arbitrary, perhaps highly overcomplete, dictionary. Recently, several "signal-space" greedy methods have been proposed to address signal recovery in this setting. However, such methods inherently rely on the existence of fast and accurate projections which allow one to identify the most relevant atoms in a dictionary for any given signal, up to a very strict accuracy. When the dictionary is highly overcomplete, no such projections are currently known; the requirements on such projections do not even hold for incoherent or well-behaved dictionaries. In this work, we provide an alternate analysis for signal space greedy methods which enforce assumptions on these projections which hold in several settings including those when the dictionary is incoherent or structurally coherent. These results align more closely with traditional results in the standard CoSa literature and improve upon previous work in the signal space setting.

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“…An image denoiser can also be part of deep network models to improve the training of high-level vision tasks [27]. However, being an ill-posed inverse problem, denoising is challenging [14].…”

Section: Introductionmentioning

confidence: 99%

Blind Universal Bayesian Image Denoising With Gaussian Noise Level Learning

Helou

Süsstrunk

2020

IEEE Trans. on Image Process.

106

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Blind and universal image denoising consists of using a unique model that denoises images with any level of noise. It is especially practical as noise levels do not need to be known when the model is developed or at test time. We propose a theoretically-grounded blind and universal deep learning image denoiser for additive Gaussian noise removal. Our network is based on an optimal denoising solution, which we call fusion denoising. It is derived theoretically with a Gaussian image prior assumption. Synthetic experiments show our network's generalization strength to unseen additive noise levels. We also adapt the fusion denoising network architecture for image denoising on real images. Our approach improves real-world grayscale additive image denoising PSNR results for training noise levels and further on noise levels not seen during training. It also improves state-of-the-art color image denoising performance on every single noise level, by an average of 0.1d B, whether trained on or not.

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Image Denoising

Cited by 5 publications

References 47 publications

Predicting Antitumor Activity of Peptides by Consensus of Regression Models Trained on a Small Data Sample

Predicting Antitumor Activity of Peptides by Consensus of Regression Models Trained on a Small Data Sample

Greedy signal space methods for incoherence and beyond

Blind Universal Bayesian Image Denoising With Gaussian Noise Level Learning

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