A nonsmooth regularization approach based on shearlets for Poisson noise removal in ROI tomography

Bubba, Tatiana A.; Porta, Federica; Zanghirati, Gaetano; Bonettini, Silvia

doi:10.1016/j.amc.2017.09.001

Cited by 14 publications

(16 citation statements)

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“…The most usually affected noises on biomedical imaging are salt and pepper (Thanh et al, 2020), speckling (Gai et al, 2018), Gaussian and Poisson noise (Bubba et al, 2018). A new noiseless image I *( a ) is formed by combining the output of Gaussian filtering, range filtering image (Kumar et al, 2012) and some white Gaussian noise.…”

Section: Literature Surveymentioning

confidence: 99%

A field programmable gate array-based biomedical noise reduction framework using advanced trilateral filter

Raja

Naveen

Palaniswamy

et al. 2021

Transactions of the Institute of Measurement and Control

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Filtering is one of the essential tools utilized to remove undesirable features in biomedical images. Most biomedical image denoising systems are used for clinical diagnosis. So, in this paper, we use the advanced trilateral filter in the field programmable gate array (FPGA) for removing noise in the biomedical image. Generally, the trilateral filter is used as an edge preserving smoothing filter. This advanced approach of trilateral filter gives the best noise diminution and enhances the image quality. This paper also proposes the hardware implementation of an efficient FPGA-based advanced trilateral filter on real time execution. In this manuscript, we intend to design and implement the FPGA architecture using an advanced trilateral filter. Biomedical images with different noises are used during implementation and compared with the existing bilateral and trilateral architecture to assess the proposed architecture performance. For evaluating the performance metrics of the proposed advanced trilateral filter on MATLAB platform, peak signal-to-noise ratio (PSNR), mean squared error (MSE) and structured similarity index (SSIM) are calculated for different biomedical images – such as brain (MRI), chest (x-ray) and lungs (CT) – with different noises – such as salt and pepper, Gaussian, Poisson and Speckle noises – compared with existing bilateral filter and trilateral filter, respectively. The proposed advanced trilateral filter implementations are checked on Virtex-6, Virtex-7 and Zynq FPGA development board using Verilog programming language in Xilinx ISE 14.5 design tools. The simulation outcomes display that the FPGA execution of the advanced trilateral filter contains better noise removal efficiency in biomedical images compared with the existing bilateral and trilateral filter.

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Section: Literature Surveymentioning

confidence: 99%

A field programmable gate array-based biomedical noise reduction framework using advanced trilateral filter

Raja

Naveen

Palaniswamy

et al. 2021

Transactions of the Institute of Measurement and Control

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“…Proof. Thanks to the source condition (S1), r † = A * µ w for some w ∈ Z: hence, we can consider w = S u w in (10) and deduce…”

Section: As a Consequencementioning

confidence: 99%

“…Sparse regularization methods from fewer tomographic measurements than usually required by standard methods (like filtered-back projection) have been widely used in tomographic reconstructions. Beside the already mentioned TV, also wavelets [43,47,49], curvelets [14,31] and -the most relevant for our work -shearlets [10,9,18,53] have been successfully applied. All these papers deal with deterministic inverse problems, and the relevance to our work is mostly numerical, for their use of sparse regularization to compensate for the subsampled data regime.…”

Section: Introductionmentioning

confidence: 99%

Shearlet-based regularization in statistical inverse learning with an application to X-ray tomography

Bubba,

Ratti

2021

Preprint

Self Cite

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Statistical inverse learning theory, a field that lies at the intersection of inverse problems and statistical learning, has lately gained more and more attention. In an effort to steer this interplay more towards the variational regularization framework, convergence rates have recently been proved for a class of convex, p-homogeneous regularizers with p ∈ (1, 2], in the symmetric Bregman distance.Following this path, we take a further step towards the study of sparsity-promoting regularization and extend the aforementioned convergence rates to work with p -norm regularization, with p ∈ (1, 2), for a special class of non-tight Banach frames, called shearlets, and possibly constrained to some convex set. The p = 1 case is approached as the limit case (1, 2) p → 1, by complementing numerical evidence with a (partial) theoretical analysis, based on arguments from Γ-convergence theory. We numerically demonstrate our theoretical results in the context of X-ray tomography, under random sampling of the imaging angles, using both simulated and measured data.

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“…This type of noise is generated when a charge carrier such as electrons or ions travel through a gap results in random fluctuation in electric current. This random fluctuation is known as shot noise [15]. (Fig.…”

Section: Poisson Noisementioning

confidence: 99%

Numerical Methods for Information Tracking of Noisy and Non-smooth Data in Large-scale Statistics

Avinash

Srisupattarawanit

Ostermeyer

2019

JERR

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In our universe, there is a presence of random bit of disorder in every field that has to be contemplated and understood clearly. This random bit of disorder in a physical system is known as noise. Noise in the field of statistics can be defined as an additional meaningless information that cannot be clearly interpreted which is present in the entire dataset. In large-scale statistics, noisy data has an adverse effect on the results and it can lead to skewness in any data analysis process, if not properly understood or handled. The adverse effect on the results is mainly due to uncorrelated (zero autocorrelation) property of noise. This makes it completely unpredictable at any given point in time, hence thorough investigation and removal of noise plays a vital role in data analysis process. In the field of engineering, measurement of experimental data obtained by using scientific instruments consists of some values that are independent of the experimental setup. One of most widely technique is the optimization methods viz, gradient descent, conjugate gradient, Newton’s method etc. Most of these methods require the determination of derivative of a function specified by the dataset (using finite-difference approximation). If the noisy data is approximated using a specific finite difference method this results in the amplification of noise present in the data. In order to overcome the aforementioned problem of amplification of noise in the derivative of a function, various regularization methods are employed. The parameter that plays a vital role in these methods are termed as regularization parameter. One of the most important technique used in the field of regularization is known as total variation regularization. This review aimed at gathering the disperse literature on the current state of various noises and their regularization methods.

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A nonsmooth regularization approach based on shearlets for Poisson noise removal in ROI tomography

Cited by 14 publications

References 50 publications

A field programmable gate array-based biomedical noise reduction framework using advanced trilateral filter

A field programmable gate array-based biomedical noise reduction framework using advanced trilateral filter

Shearlet-based regularization in statistical inverse learning with an application to X-ray tomography

Numerical Methods for Information Tracking of Noisy and Non-smooth Data in Large-scale Statistics

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