scholarly journals Reconstruction Method for Optical Tomography Based on the Linearized Bregman Iteration with Sparse Regularization

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Chengcai Leng ◽  
Dongdong Yu ◽  
Shuang Zhang ◽  
Yu An ◽  
Yifang Hu
Keyword(s):  
A Priori ◽  
Optical Tomography ◽  
Reconstruction Method ◽  
Bregman Iteration ◽  
Sparse Regularization ◽  
Bioluminescence Tomography ◽  
Regularization Problem ◽  
Ill Posed ◽  
Linearized Bregman Iteration

Optical molecular imaging is a promising technique and has been widely used in physiology, and pathology at cellular and molecular levels, which includes different modalities such as bioluminescence tomography, fluorescence molecular tomography and Cerenkov luminescence tomography. The inverse problem is ill-posed for the above modalities, which cause a nonunique solution. In this paper, we propose an effective reconstruction method based on the linearized Bregman iterative algorithm with sparse regularization (LBSR) for reconstruction. Considering the sparsity characteristics of the reconstructed sources, the sparsity can be regarded as a kind ofa prioriinformation and sparse regularization is incorporated, which can accurately locate the position of the source. The linearized Bregman iteration method is exploited to minimize the sparse regularization problem so as to further achieve fast and accurate reconstruction results. Experimental results in a numerical simulation andin vivomouse demonstrate the effectiveness and potential of the proposed method.

scholarly journals Hybrid Multilevel Sparse Reconstruction for a Whole Domain Bioluminescence Tomography Using Adaptive Finite Element

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jingjing Yu ◽  
Xiaowei He ◽  
Guohua Geng ◽  
Fang Liu ◽  
L. C. Jiao
Keyword(s):  
Finite Element ◽  
Adaptive Finite Element Method ◽  
Source Distribution ◽  
Adaptive Finite Element ◽  
Sparse Regularization ◽  
Bioluminescence Tomography ◽  
Reconstruction Scheme ◽  
Boundary Measurements ◽  
Ill Posed

Quantitative reconstruction of bioluminescent sources from boundary measurements is a challenging ill-posed inverse problem owing to the high degree of absorption and scattering of light through tissue. We present a hybrid multilevel reconstruction scheme by combining the ability of sparse regularization with the advantage of adaptive finite element method. In view of the characteristics of different discretization levels, two different inversion algorithms are employed on the initial coarse mesh and the succeeding ones to strike a balance between stability and efficiency. Numerical experiment results with a digital mouse model demonstrate that the proposed scheme can accurately localize and quantify source distribution while maintaining reconstruction stability and computational economy. The effectiveness of this hybrid reconstruction scheme is further confirmed within vivoexperiments.

scholarly journals A Sparsity-Constrained Preconditioned Kaczmarz Reconstruction Method for Fluorescence Molecular Tomography

2016 ◽  
Vol 2016 ◽  
pp. 1-15
Author(s):  
Duofan Chen ◽  
Jimin Liang ◽  
Yao Li ◽  
Guanghui Qiu
Keyword(s):  
Low Cost ◽  
Biological Tissues ◽  
Reconstruction Method ◽  
Fluorescence Molecular Tomography ◽  
In Vivo Experiments ◽  
Fluorescent Markers ◽  
Ill Posed ◽  
Kaczmarz Method ◽  
Memory Efficient

Fluorescence molecular tomography (FMT) is an imaging technique that can localize and quantify fluorescent markers to resolve biological processes at molecular and cellular levels. Owing to a limited number of measurements and a large number of unknowns as well as the diffusive transport of photons in biological tissues, the inverse problem in FMT is usually highly ill-posed. In this work, a sparsity-constrained preconditioned Kaczmarz (SCP-Kaczmarz) method is proposed to reconstruct the fluorescent target for FMT. The SCP-Kaczmarz method uses the preconditioning strategy to minimize the correlation between the rows of the forward matrix and constrains the Kaczmarz iteration results to be sparse. Numerical simulation and phantom and in vivo experiments were performed to test the efficiency of the proposed method. The results demonstrate that both the convergence and accuracy of the proposed method are improved compared with the classical memory-efficient low-cost Kaczmarz method.

Reconstruction Method for In Vivo Bioluminescence Tomography Based on the Split Bregman Iterative and Surrogate Functions

2016 ◽  
Vol 19 (2) ◽  
pp. 245-255 ◽  
Author(s):  
Shuang Zhang ◽  
Kun Wang ◽  
Hongbo Liu ◽  
Chengcai Leng ◽  
Yuan Gao ◽  
...  
Keyword(s):  
Reconstruction Method ◽  
Split Bregman ◽  
Bioluminescence Tomography ◽  
Surrogate Functions

scholarly journals Complex wavefront sensing based on coherent diffraction imaging using vortex modulation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Rujia Li ◽  
Liangcai Cao
Keyword(s):  
Phase Retrieval ◽  
Dynamic Range ◽  
A Priori ◽  
Measured Intensity ◽  
Physical Constraints ◽  
Coherent Diffraction Imaging ◽  
Effective Dynamic ◽  
Ill Posed ◽  
Retrieval Problem ◽  
Diffraction Imaging

AbstractPhase retrieval seeks to reconstruct the phase from the measured intensity, which is an ill-posed problem. A phase retrieval problem can be solved with physical constraints by modulating the investigated complex wavefront. Orbital angular momentum has been recently employed as a type of reliable modulation. The topological charge l is robust during propagation when there is atmospheric turbulence. In this work, topological modulation is used to solve the phase retrieval problem. Topological modulation offers an effective dynamic range of intensity constraints for reconstruction. The maximum intensity value of the spectrum is reduced by a factor of 173 under topological modulation when l is 50. The phase is iteratively reconstructed without a priori knowledge. The stagnation problem during the iteration can be avoided using multiple topological modulations.

scholarly journals Aerosol-based antimicrobial photoinactivation in the lungs: an action spectrum study

2021 ◽  
Author(s):  
Chiara Treghini ◽  
Alfonso Dell’Accio ◽  
Franco Fusi ◽  
Giovanni Romano
Keyword(s):  
Light Source ◽  
A Priori ◽  
Action Spectrum ◽  
Multidrug Resistant ◽  
Theoretical Modelling ◽  
Resistant Bacteria ◽  
Lung Infections ◽  
Killing Action ◽  
Definition Of

AbstractChronic lung infections are among the most diffused human infections, being often associated with multidrug-resistant bacteria. In this framework, the European project “Light4Lungs” aims at synthesizing and testing an inhalable light source to control lung infections by antimicrobial photoinactivation (aPDI), addressing endogenous photosensitizers only (porphyrins) in the representative case of S. aureus and P. aeruginosa. In the search for the best emission characteristics for the aerosolized light source, this work defines and calculates the photo-killing action spectrum for lung aPDI in the exemplary case of cystic fibrosis. This was obtained by applying a semi-theoretical modelling with Monte Carlo simulations, according to previously published methodology related to stomach infections and applied to the infected trachea, bronchi, bronchioles and alveoli. In each of these regions, the two low and high oxygen concentration cases were considered to account for the variability of in vivo conditions, together with the presence of endogenous porphyrins and other relevant absorbers/diffusers inside the illuminated biofilm/mucous layer. Furthermore, an a priori method to obtain the “best illumination wavelengths” was defined, starting from maximizing porphyrin and light absorption at any depth. The obtained action spectrum is peaked at 394 nm and mostly follows porphyrin extinction coefficient behavior. This is confirmed by the results from the best illumination wavelengths, which reinforces the robustness of our approach. These results can offer important indications for the synthesis of the aerosolized light source and definition of its most effective emission spectrum, suggesting a flexible platform to be considered in further applications.

scholarly journals Regularization of backward time-fractional parabolic equations by Sobolev-type equations

2020 ◽  
Vol 28 (5) ◽  
pp. 659-676
Author(s):  
Dinh Nho Hào ◽  
Nguyen Van Duc ◽  
Nguyen Van Thang ◽  
Nguyen Trung Thành
Keyword(s):  
Error Estimates ◽  
Parabolic Equations ◽  
Regularization Parameter ◽  
A Priori ◽  
Sobolev Type ◽  
A Posteriori ◽  
Parameter Choice ◽  
Numerical Tests ◽  
Ill Posed ◽  
Parameter Choice Rules

AbstractThe problem of determining the initial condition from noisy final observations in time-fractional parabolic equations is considered. This problem is well known to be ill-posed, and it is regularized by backward Sobolev-type equations. Error estimates of Hölder type are obtained with a priori and a posteriori regularization parameter choice rules. The proposed regularization method results in a stable noniterative numerical scheme. The theoretical error estimates are confirmed by numerical tests for one- and two-dimensional equations.

Acceleration of the EM-like reconstruction method for diffuse optical tomography with ordered-subsets method

2014 ◽  
Vol 22 (3) ◽  
Author(s):  
Caifang Wang
Keyword(s):  
Numerical Experiments ◽  
Imaging Modality ◽  
Random Medium ◽  
Optical Tomography ◽  
Back Propagation ◽  
Three Dimensional ◽  
Diffuse Optical Tomography ◽  
Optical Parameters ◽  
Reconstruction Method ◽  
Boundary Measurements

Abstract.Diffuse optical tomography (DOT) is an optical imaging modality, which provides the spatial distribution of the optical parameters inside a random medium. A propagation back-propagation method named EM-like reconstruction method for stationary DOT problem has been proposed yet. This method is really time consuming. Hence the ordered-subsets (OS) technique for this reconstruction method is studied in this paper. The boundary measurements of DOT are grouped into nonoverlapping and overlapping ordered sequence of subsets with random partition, sequential partition and periodic partition, respectively. The performance of OS methods is compared with the standard EM-like reconstruction method with two-dimensional and three-dimensional numerical experiments. The numerical experiments indicate that reconstruction of nonoverlapping subsets with periodic partition, overlapping subsets with periodic partition and standard EM-like method provide very similar acceptable reconstruction results. However, reconstruction of nonoverlapping subsets with periodic partition spends a minimum of time to get proper results.

scholarly journals The Regularized Weak Functional Matching Pursuit for linear inverse problems

2019 ◽  
Vol 27 (3) ◽  
pp. 317-340 ◽  
Author(s):  
Max Kontak ◽  
Volker Michel
Keyword(s):  
Inverse Problems ◽  
Matching Pursuit ◽  
A Priori ◽  
Computation Time ◽  
Point Of View ◽  
Computational Point ◽  
Linear Inverse Problems ◽  
Infinite Dimensional ◽  
Frame Condition ◽  
Ill Posed

Abstract In this work, we present the so-called Regularized Weak Functional Matching Pursuit (RWFMP) algorithm, which is a weak greedy algorithm for linear ill-posed inverse problems. In comparison to the Regularized Functional Matching Pursuit (RFMP), on which it is based, the RWFMP possesses an improved theoretical analysis including the guaranteed existence of the iterates, the convergence of the algorithm for inverse problems in infinite-dimensional Hilbert spaces, and a convergence rate, which is also valid for the particular case of the RFMP. Another improvement is the cancellation of the previously required and difficult to verify semi-frame condition. Furthermore, we provide an a-priori parameter choice rule for the RWFMP, which yields a convergent regularization. Finally, we will give a numerical example, which shows that the “weak” approach is also beneficial from the computational point of view. By applying an improved search strategy in the algorithm, which is motivated by the weak approach, we can save up to 90  of computation time in comparison to the RFMP, whereas the accuracy of the solution does not change as much.

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