Compressive Imaging via Approximate Message Passing With Image Denoising

Tan, Jin; Ma, Yanting; Baron, Dror

doi:10.1109/tsp.2015.2408558

Cited by 79 publications

(65 citation statements)

References 37 publications

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“…Note that the decay of the bias term mirrors the decay of the Fourier coefficients of f , by (53). In particular, if f is smooth, its Fourier coefficients decay faster, and hence the bias decays rapidly with J.…”

Section: 2mentioning

confidence: 92%

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Statistical estimation: from denoising to sparse regression and hidden cliques

Tramel¹,

Kumar²,

Giurgiu³

et al. 2015

Statistical Physics, Optimization, Inference, and Message-Passing Algorithms

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Abstract. These notes review six lectures given by Prof. Andrea Montanari on the topic of statistical estimation for linear models. The first two lectures cover the principles of signal recovery from linear measurements in terms of minimax risk. Subsequent lectures demonstrate the application of these principles to several practical problems in science and engineering. Specifically, these topics include denoising of error-laden signals, recovery of compressively sensed signals, reconstruction of low-rank matrices, and also the discovery of hidden cliques within large networks.These are notes from the lecture of Andrea Montanari given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches,

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Section: 2mentioning

confidence: 92%

“…Indeed similar ideas were developed and applied to a large number of problems, see [49,49,50,7,51,52,53,54] for a a very incomplete list of examples.…”

Section: Message Passing Algorithmsmentioning

confidence: 99%

Statistical estimation: from denoising to sparse regression and hidden cliques

Tramel¹,

Kumar²,

Giurgiu³

et al. 2015

Statistical Physics, Optimization, Inference, and Message-Passing Algorithms

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“…Its contribution to improving the tradeoff between sparsity and undersampling rate has been shown in [4]. Initially proposed for signal reconstruction, AMP has been extended to images in [10], by performing the denoising in the wavelet domain.…”

Section: Basics Of Approximate Message Passingmentioning

confidence: 99%

“…As a result, the input data of the denoising η t (·) function is DΘ * z t + θ t x . The implementation of the proposed iterative algorithm summarized in (7) and (8) is based on [10]. The initialization consists in setting x t to a zero-vector, and subsequently calculate z t , i.e.…”

Section: Amp-based Ultrasound Image Reconstructionmentioning

confidence: 99%

Ultrasound image reconstruction from compressed measurements using approximate message passing

Kim

Basarab

Hill

et al. 2016

2016 24th European Signal Processing Conference (EUSIPCO)

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 17008The contribution was presented at EUSIPCO 2016 :http://www.eusipco2016.org/ ABSTRACTIn this paper we propose a novel framework for compressive sampling reconstruction of biomedical ultrasonic images based on the Approximate Message Passing (AMP) algorithm. AMP is an iterative algorithm that performs image reconstruction through image denoising within a compressive sampling framework. In this work, our aim is to evaluate the merits of several combinations of a denoiser and a transform domain, which are the two main factors that determine the recovery performance. In particular, we investigate reconstruction performance in the spatial, DCT, and wavelet domains. We compare the results with existing reconstruction algorithms already used in ultrasound imaging and quantify the performance improvement.

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“…Owing to the fact that image prior knowledge plays a critical role in the performance of compressive sensing reconstruction, much efforts have been made to develop an effective regularization term or signal model to reflect the image prior knowledge. Standard CS methods exploit the sparsity of signal in some domains, such as DCT [3], wavelets [4,5], total variation (TV) [6,7], and learned dictionary [8,9]. Unfortunately, these methods are less appropriate for many imaging applications.…”

Section: Introductionmentioning

confidence: 99%

Content-Aware Compressive Sensing Recovery Using Laplacian Scale Mixture Priors and Side Information

Xie

Liu

2018

Mathematical Problems in Engineering

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Nonlocal methods have shown great potential in many image restoration tasks including compressive sensing (CS) reconstruction through use of image self-similarity prior. However, they are still limited in recovering fine-scale details and sharp features, when rich repetitive patterns cannot be guaranteed; moreover the CS measurements are corrupted. In this paper, we propose a novel CS recovery algorithm that combines nonlocal sparsity with local and global prior, which soften and complement the selfsimilarity assumption for irregular structures. First, a Laplacian scale mixture (LSM) prior is utilized to model dependencies among similar patches. For achieving group sparsity, each singular value of similar packed patches is modeled as a Laplacian distribution with a variable scale parameter. Second, a global prior and a compensation-based sparsity prior of local patch are designed in order to maintain differences between packed patches. The former refers to a prediction which integrates the information at the independent processing stage and is used as side information, while the latter enforces a small (i.e., sparse) prediction error and is also modeled with the LSM model so as to obtain local sparsity. Afterward, we derive an efficient algorithm based on the expectationmaximization (EM) and approximate message passing (AMP) frame for the maximum a posteriori (MAP) estimation of the sparse coefficients. Numerical experiments show that the proposed method outperforms many CS recovery algorithms.

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Compressive Imaging via Approximate Message Passing With Image Denoising

Cited by 79 publications

References 37 publications

Statistical estimation: from denoising to sparse regression and hidden cliques

Statistical estimation: from denoising to sparse regression and hidden cliques

Ultrasound image reconstruction from compressed measurements using approximate message passing

Content-Aware Compressive Sensing Recovery Using Laplacian Scale Mixture Priors and Side Information

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