Blind inverse problems with isolated spikes

Debarnot, Valentin; Weiss, Pierre

doi:10.1093/imaiai/iaac015

Cited by 3 publications

(4 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We place ourselves in the case of the recovery of one spike (note that this case is often very informative for the study of limits of super-resolution algorithms [19,38]). Results on basins of attractions show that if the descent is initialized sufficiently close to the observed spike, then under the RIP condition there will be convergence to the desired position (at a linear rate).…”

Section: Presentation Of the Experimentsmentioning

confidence: 99%

Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application

Bénard,

Traonmilin,

Aujol

et al. 2024

Inverse Problems

View full text Add to dashboard Cite

In this article, we study the problem of recovering sparse spikes with over-parametrized projected descent. We first provide a theoretical study of approximate recovery with our chosen initialization method: Continuous Orthogonal Matching Pursuit without Sliding. Then we study the effect of over-parametrization on the gradient descent which highlights the benefits of the projection step. Finally, we show the improved calculation times of our algorithm compared to state-of-the-art model-based methods on realistic simulated microscopy data.

show abstract

Section: Presentation Of the Experimentsmentioning

confidence: 99%

Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application

Bénard,

Traonmilin,

Aujol

et al. 2024

Inverse Problems

View full text Add to dashboard Cite

show abstract

“…The condition (Cond 1 ) is strongly connected to the Cramér-Rao lower-bound. Using assumptions (10) and (11), we obtain…”

Section: Relationship To Cramér-raomentioning

confidence: 99%

“…□ Let us assume that R > RL 2 . Without loss of generality, we can also assume that R µ ⩽ RL 2 , since the inequalities in (11) are still valid when replacing B Rµ by B R ′ with R ′ ⩽ R µ . In this setting, the success condition…”

Section: Lemma D1 (Expectation and Tail Bounds For The Supremum)mentioning

confidence: 99%

“…To the best of our knowledge, deriving theoretical upper-bounds remains an open research area that is at the heart of the present work. One of the authors recently conducted a similar study in [8], for the case of blind inverse problems with unknown weights. However, the proof was suboptimal and did not allow us to reach the Cramér-Rao bound asymptotically when σ → 0, contrarily to the present work.…”

Section: A Brief Tour Of Existing Performance Boundsmentioning

confidence: 99%

See 1 more Smart Citation

The MLE is a reliable source: sharp performance guarantees for localization problems

Munier,

Soubies,

Weiss

2023

Inverse Problems

Self Cite

View full text Add to dashboard Cite

Single source localization from low-pass filtered measurements is ubiquitous in optics, wireless communications and sound processing. We analyse the performance of the maximum likelihood estimator (MLE) in this context with additive white Gaussian noise.We derive necessary conditions and sufficient conditions on the maximum admissible noise level to reach a given precision with high probability. The two conditions match closely, with a discrepancy related to the conditioning of a noiseless cost function.They tightly surround the Cramer-Rao lower bound for low noise levels. However, they are significantly more precise to describe the performance of the MLE for larger levels.

show abstract

Deep-blur: Blind identification and deblurring with convolutional neural networks

Debarnot,

Weiss

2024

Biol. Imaging

View full text Add to dashboard Cite

We propose a neural network architecture and a training procedure to estimate blurring operators and deblur images from a single degraded image. Our key assumption is that the forward operators can be parameterized by a low-dimensional vector. The models we consider include a description of the point spread function with Zernike polynomials in the pupil plane or product-convolution expansions, which incorporate space-varying operators. Numerical experiments show that the proposed method can accurately and robustly recover the blur parameters even for large noise levels. For a convolution model, the average signal-to-noise ratio of the recovered point spread function ranges from 13 dB in the noiseless regime to 8 dB in the high-noise regime. In comparison, the tested alternatives yield negative values. This operator estimate can then be used as an input for an unrolled neural network to deblur the image. Quantitative experiments on synthetic data demonstrate that this method outperforms other commonly used methods both perceptually and in terms of SSIM. The algorithm can process a 512 $ \times $ 512 image under a second on a consumer graphics card and does not require any human interaction once the operator parameterization has been set up.1

show abstract

Blind inverse problems with isolated spikes

Cited by 3 publications

References 49 publications

Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application

Estimation of off-the grid sparse spikes with over-parametrized projected gradient descent: theory and application

The MLE is a reliable source: sharp performance guarantees for localization problems

Deep-blur: Blind identification and deblurring with convolutional neural networks

Contact Info

Product

Resources

About