scholarly journals Nearly Exact Discrepancy Principle for Low-Count Poisson Image Restoration

2021 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Francesca Bevilacqua ◽  
Alessandro Lanza ◽  
Monica Pragliola ◽  
Fiorella Sgallari
Keyword(s):  
Regularization Parameter ◽  
Poor Performance ◽  
Expected Value ◽  
Poisson Noise ◽  
Least Square ◽  
Discrepancy Principle ◽  
High Count ◽  
Theoretical Derivation ◽  
A Value ◽  
Data Term

The effectiveness of variational methods for restoring images corrupted by Poisson noise strongly depends on the suitable selection of the regularization parameter balancing the effect of the regulation term(s) and the generalized Kullback–Liebler divergence data term. One of the approaches still commonly used today for choosing the parameter is the discrepancy principle proposed by Zanella et al. in a seminal work. It relies on imposing a value of the data term approximately equal to its expected value and works well for mid- and high-count Poisson noise corruptions. However, the series truncation approximation used in the theoretical derivation of the expected value leads to poor performance for low-count Poisson noise. In this paper, we highlight the theoretical limits of the approach and then propose a nearly exact version of it based on Monte Carlo simulation and weighted least-square fitting. Several numerical experiments are presented, proving beyond doubt that in the low-count Poisson regime, the proposed modified, nearly exact discrepancy principle performs far better than the original, approximated one by Zanella et al., whereas it works similarly or slightly better in the mid- and high-count regimes.

Compact discrepancy and chi-squared principles for over-determined inverse problems

2017 ◽  
Vol 25 (3) ◽  
Author(s):  
Maxim Pisarenco ◽  
Irwan D. Setija
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Regularization Parameter ◽  
Discrepancy Principle ◽  
Chi Squared

AbstractWe discuss and analyze the classical discrepancy principle and the recently proposed and closely related chi-squared principle for selecting the regularization parameter of an inverse problem. Some properties that deteriorate the performance of these methods for over-determined inverse problems are highlighted. We propose a so-called

A conjugate gradient least square based method for sound field control

2021 ◽  
Vol 263 (5) ◽  
pp. 1029-1040
Author(s):  
Pierangelo Libianchi ◽  
Finn T. Agerkvist ◽  
Elena Shabalina
Keyword(s):  
Conjugate Gradient ◽  
Regularization Parameter ◽  
Sound Field ◽  
Least Square ◽  
Active Set ◽  
Noise Sources ◽  
Field Control ◽  
Ill Posed ◽  
The Right ◽  
Number Of Iterations

In sound field control, a set of control sources is used to match the pressure field generated by noise sources but with opposite phase to reduce the total sound pressure level in a defined area commonly referred to as dark zone. This is usually an ill-posed problem. The approach presented here employs a subspace iterative method where the number of iterations acts as the regularization parameter and controls unwanted side radiation, i.e. side lobes. More iterations lead to less regularization and more side lobes. The number of iterations is controlled by problem-specific stopping criteria. Simulations show the increase of lobing with increased number of iterations. The solutions are analysed through projections on the basis provided by the source strength modes corresponding to the right singular vector of the transfer function matrix. These projections show how higher order pressure modes (left singular vectors) become dominant with larger number of iterations. Furthermore, an active-set type method provides the constraints on the amplitude of the solution which is not possible with the conjugate gradient least square algorithm alone.

scholarly journals Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 608
Author(s):  
Pornsarp Pornsawad ◽  
Parada Sungcharoen ◽  
Christine Böckmann
Keyword(s):  
Convergence Rate ◽  
Potential Problem ◽  
Regularization Parameter ◽  
Discrepancy Principle ◽  
Source Condition ◽  
Rate Analysis ◽  
Potential Problems ◽  
Ill Posed ◽  
Landweber Method ◽  
Convergence Rate Analysis

In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.

scholarly journals The Impact of the Discrepancy Principle on the Tikhonov-Regularized Solutions with Oversmoothing Penalties

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 331
Author(s):  
Bernd Hofmann ◽  
Christopher Hofmann
Keyword(s):  
Case Studies ◽  
Convergence Rates ◽  
Regularization Parameter ◽  
A Priori ◽  
Discrepancy Principle ◽  
Parameter Choice ◽  
Operator Equations ◽  
Analytical Results ◽  
Ill Posed ◽  
The Impact

This paper deals with the Tikhonov regularization for nonlinear ill-posed operator equations in Hilbert scales with oversmoothing penalties. One focus is on the application of the discrepancy principle for choosing the regularization parameter and its consequences. Numerical case studies are performed in order to complement analytical results concerning the oversmoothing situation. For example, case studies are presented for exact solutions of Hölder type smoothness with a low Hölder exponent. Moreover, the regularization parameter choice using the discrepancy principle, for which rate results are proven in the oversmoothing case in in reference (Hofmann, B.; Mathé, P. Inverse Probl. 2018, 34, 015007) is compared to Hölder type a priori choices. On the other hand, well-known analytical results on the existence and convergence of regularized solutions are summarized and partially augmented. In particular, a sketch for a novel proof to derive Hölder convergence rates in the case of oversmoothing penalties is given, extending ideas from in reference (Hofmann, B.; Plato, R. ETNA. 2020, 93).

scholarly journals Group velocity maps using subspace and Trans-dimensional inversions: ambient noise tomography in the Western part of Java, Indonesia

2019 ◽  
Author(s):  
Shindy Rosalia ◽  
Phil Cummins ◽  
Sri Widiyantoro ◽  
Tedi Yudistira ◽  
Andri Dian Nugraha ◽  
...  
Keyword(s):  
Rayleigh Wave ◽  
Group Velocity ◽  
Ambient Noise ◽  
Regularization Parameter ◽  
Least Square ◽  
Disaster Mitigation ◽  
Wave Group ◽  
Ambient Noise Tomography ◽  
Waveform Data ◽  
Subspace Optimization

Summary In this paper, we compare two different methods for group velocity inversion: iterative, least-squares subspace optimization, and probabilistic sampling based on the Trans-dimensional Bayesian method with tree-based wavelet parameterization. The wavelet parameterization used a hierarchical prior for wavelet coefficients which could adapt to the data. We applied these inversion methods for ambient noise tomography of the western part of Java, Indonesia. This area is an area prone to multiple geological hazards due to its proximity to the subduction of the Australia Plate beneath Eurasia. It is therefore important to have a better understanding of upper crustal structure to support seismic hazard and disaster mitigation efforts in this area. We utilized a new waveform dataset collected from 85 temporary seismometers deployed during 2016–2018. Cross-correlation of the waveform data was applied to retrieve empirical Rayleigh wave Green's functions between station pairs, and the spatial distribution of group velocity was obtained by inverting dispersion curves. Our results show that, although computationally expensive, the Trans-dimensional Bayesian approach offered important advantages over optimization, including more effective explorative of the model space and more robust characterization of the spatial pattern of Rayleigh wave group velocity. Meanwhile, the iterative, least-square subspace optimization suffered from the subjectivity of choice for reference velocity model and regularization parameter values. Our Rayleigh wave group velocity results show that for short (1–10 s) periods group velocity correlates well with surface geology, and for longer periods (13–25 s) it correlates with centers of volcanic activity.

scholarly journals The Antecedents and Consequences of Value Co-Creation Behaviors in a Hotel Setting: A Two-Country Study

2019 ◽  
Vol 61 (3) ◽  
pp. 353-368 ◽  
Author(s):  
Sanjit K. Roy ◽  
M. S. Balaji ◽  
Geoffrey Soutar ◽  
Yangyang Jiang
Keyword(s):  
Well Being ◽  
The United States ◽  
Partial Least Square ◽  
Least Square ◽  
Service Encounters ◽  
Online Questionnaire ◽  
Fairness Perception ◽  
A Value ◽  
Country Study ◽  
Antecedents And Consequences

This study examines the antecedents and consequences of value co-creation behavior in a hospitality context. An online questionnaire with samples of hotel patrons in the United States and Australia was used to obtain data and partial least square modeling was used in the analysis. The results suggest patron fairness perception enhances trust and identification with a hotel, which encourage engagement in the value co-creation behavior. Furthermore, this behavior enhances patron well-being and respect for the hotel. The study contributes to the literature by suggesting a value co-creation behavior model in the hospitality context and empirically examining the antecedents and consequences of this behavior. The results have important implications for managers designing service encounters that can encourage hotel patrons to engage in the value co-creation behavior.

scholarly journals Interaction effect between product and process innovation: the case of Tunisian banks

2016 ◽  
Vol 11 (1) ◽  
pp. 60-70 ◽  
Author(s):  
Mabrouk Abir ◽  
Dhouibi Raoudha ◽  
Rouetbi Emna
Keyword(s):  
Interaction Effect ◽  
Financial Services ◽  
Financial Innovation ◽  
Poor Performance ◽  
Process Innovation ◽  
Bank Performance ◽  
A Value ◽  
Product And Process Innovation ◽  
Product And Process ◽  
The Impact

The authors examine the impact of the relationship between two types of financial innovation and bank performance. The research attempts to test hypotheses that are not yet validated by previous studies focusing on the financial services industry, thus, giving the study an exploratory look. The authors try, specifically, to determine the interaction effect of both types of financial innovation on bank performance and, then, try to enrich innovation theory with new hypotheses on product and process innovation. The results show that Tunisian banks have begun, probably, to see the importance or the need for the simultaneous adoption of two types of financial innovation since 1995 to improve their poor performance. The authors also find that the interaction effect of product and process innovation reduces profitability. However, efficiency is achieved in terms of market share and value. The authors conclude that financial innovation is a value creation instrument for Tunisian banks

scholarly journals The Implementation of Organizational Culture Based on Tri Hita Karana in the Effort to Realize the Organizational Performance in PDAM Buleleng Regency

2019 ◽  
Vol 3 (2) ◽  
pp. 77
Author(s):  
Luh Kartika Ningsih ◽  
Ni Luh Putu Eka Yudi Prastiwi ◽  
Ni Made Sri Ayuni
Keyword(s):  
Organizational Culture ◽  
Quality Management ◽  
Total Quality Management ◽  
Organizational Performance ◽  
Employee Performance ◽  
Partial Least Square ◽  
Least Square ◽  
Total Quality ◽  
A Value

This study aims to determine the role of Organizational Culture based on Tri Hita Karana in the effort to realize Organizational Performance by taking into account other factors such as Human Resource Management, Total Quality Management, and Employee Performance. This study uses a quantitative approach. The data analysis technique used in this study is a structural equation model (SEM) based on variance or Component based SEM, known as Partial Least Square (PLS) Visual version 3.2.7. The number of samples used was 48 people with t-table values for significance levels α = 0.05 and degree of freedom (df) = 46 is 2.58. The results show that there are two relationships that show significant results, namely the role of Organizational Culture based on Tri Hita Karana on Employee Performance has a value of 17.353 with t-statistics > t-table (17.353 > 2.58). And the same results are also shown in the relationship between Total Quality Management and Organizational Performance with a value of 8.232 > 2.58. Different results are shown in 4 other relationships, namely the influence of the organization's culture on organizational performance, the influence of HRM on organizational performance, the influence of HRM on employee performance, and the influence of total quality management on employee performance with t-statistics < t- table (0.220 < 2.58), (0.544 < 2.58), (0.866 < 2.58), and (0.553 < 2.58). From the results of this study it can be seen that there are still several factors that have not been able to provide a significant value on organizational performance in the PDAM Buleleng.

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