The interior inverse scattering problem for a two-layered cavity using the Bayesian method

Yin, Yunwen; Yin, Weishi; Meng, Pinchao; Liu, Hongyu

doi:10.3934/ipi.2021069

Cited by 21 publications

(6 citation statements)

References 27 publications

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“…This advanced imaging could unravel the neurobiological complexities of schizophrenia, enhancing our understanding of the disorder. The Bayesian method for interior inverse scattering, as proposed by Yin et al, [ 18 ] could further refine our analysis, enabling the reconstruction of intricate neural interfaces. This integrated approach, combining detailed therapy component analysis with sophisticated imaging technology, promises a significant leap forward in understanding and treating schizophrenia, offering valuable insights into its pathophysiology and informing the development of targeted therapies.…”

Section: Discussionmentioning

confidence: 98%

Clinical study of dance art therapy on hospitalized patients with chronic schizophrenia

Kong,

Min,

Zhu

et al. 2024

Medicine

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Background: To explore the effect of dance art on the treatment of hospitalized patients with chronic schizophrenia. Methods: In a prospective randomized controlled study conducted from June 2019 to June 2020, 120 patients from Shanghai Pudong New Area Mental Health Center were divided into intervention (n = 60) and control (n = 60) groups using a random number table. Control patients received standard drug treatment and nursing care, while the intervention group underwent dance art therapy sessions for 90 minutes twice weekly, in addition to standard care. Treatment outcomes after 6 and 12 weeks were measured using the positive and negative symptom scale (PANSS), Wisconsin Card Sorting Test (WCST), Montreal Cognitive Assessment Scale (MoCA), and body mass index (BMI). Results: This study involved 120 male patients with chronic schizophrenia, aged 30 to 60 years. After 6 and 12 weeks, the intervention group showed a greater reduction in PANSS scores (intervention group: from 49.02 ± 2.53 to 37.02 ± 1.83, control group: from 49.08 ± 2.59 to 44.91 ± 2.35, P < .05). In the WCST, the intervention group exhibited a higher increase in classification completion and correct answers, and a greater decrease in errors (P < .05). MoCA scores improved significantly in the intervention group compared to the control group (P < .05). BMI decreased in both groups, with a more pronounced reduction in the intervention group (intervention group: from 26.47 ± 1.05 kg/m² to 22.87 ± 0.73 kg/m², control group: from 26.50 ± 1.03 kg/m² to 26.22 ± 0.80 kg/m², P < .05). Conclusion: Based on routine drug treatment and routine nursing care, dance art has a better clinical effect in treating hospitalized patients with chronic schizophrenia, which can improve cognitive function, alleviate clinical symptoms, and reduce BMI.

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Section: Discussionmentioning

confidence: 98%

Clinical study of dance art therapy on hospitalized patients with chronic schizophrenia

Kong,

Min,

Zhu

et al. 2024

Medicine

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“…In this paper, we consider a Bayesian approach that captures this idea for two parametrizations used in detection of inclusions for nonlinear inverse problems: the star-shaped set and level set parametrizations. These parametrizations are studied rigorously in [9][10][11] and remain popular to Bayesian practitioners: we mention [1,[12][13][14][15][16] in the case of the star-shaped inclusions and [12,[17][18][19][20][21] for the level set inclusions, see also references therein.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian approach for consistent reconstruction of inclusions

Afkham,

Knudsen,

Rasmussen

et al. 2024

Inverse Problems

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This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of the corresponding posterior distributions in a small measurement noise limit. The methodology is general; it works for priors arising from any Hölder continuous transformation of Gaussian random fields and is applicable to a range of inverse problems.  The level set and star-shaped prior distributions are examples of push-forward priors under Hölder continuous transformations that take advantage of the structure of inclusion detection problems.  We show that the corresponding posterior mean converges to the ground truth in a proper probabilistic sense. Numerical tests on a two-dimensional quantitative photoacoustic tomography problem showcase the approach. The results highlight the convergence properties of the posterior distributions and the ability of the methodology to detect inclusions with sufficiently regular boundaries.

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“…However, for the general shape of the cavity, the uniqueness result using one single point source is still a challenging open problem, although Qin and Cakoni [38] gave a uniqueness analysis under certain geometric assumptions. In numerics, various reconstruction algorithms were proposed to solve the inverse cavity scattering problems, such as the linear sampling method [15,39,40,42], the regularized Newton iterative method [38,41], the decomposition method [47], the factorization method [33], the reciprocity gap functional method [43], and the machine learning method [16,44]. These methods have been also applied to a variety of inverse problems for elastic wave and electromagnetic waves and electrostatics; see [2,11,13,28,35,36,45,46].…”

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confidence: 99%

“…The former mainly refers to the sampling method and its variants [9,10,15,23,33,39,40,42,43,49,50], which do not require a priori information about the geometry and boundary condition of the problem, but need measured data corresponding to a large number of incident waves. The latter includes the linearization approximation [10], the iterative method [5,41,48] and the machine learning method [16,44], which requires some a priori information to obtain the initial approximation or to place the auxiliary object, but often uses only one or several incident waves.…”

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confidence: 99%

Numerical method for the inverse interior scattering problem from phaseless data

Li,

Lv,

Wang

2024

IPI

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This paper is concerned with the inverse problem to determine the shape and location of an acoustically sound-soft cavity, or sound-hard cavity, or impedance cavity with known impedance function from phaseless data for one single source incidence. Based on representing scattered field by single-layer potential, a numerical method is presented for finding the unknown boundary of scatterers. Furthermore, we propose a Newton-type algorithm to recover a realvalued surface impedance from phaseless data. The efficient implementation of the method is described and the feasibility of the approach is illustrated by several numerical examples.

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The interior inverse scattering problem for a two-layered cavity using the Bayesian method

Cited by 21 publications

References 27 publications

Clinical study of dance art therapy on hospitalized patients with chronic schizophrenia

Clinical study of dance art therapy on hospitalized patients with chronic schizophrenia

A Bayesian approach for consistent reconstruction of inclusions

Numerical method for the inverse interior scattering problem from phaseless data

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