scholarly journals Spatial Domain Terahertz Image Reconstruction Based on Dual Sparsity Constraints

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4116
Author(s):  
Xiaozhen Ren ◽  
Yuying Jiang
Keyword(s):  
Image Reconstruction ◽  
Optimization Problem ◽  
Separation Of Variables ◽  
Sampling Rate ◽  
Acquisition Time ◽  
Split Bregman ◽  
Edge Preserving ◽  
Reconstruction Quality ◽  
Sparsity Constraints ◽  
Reconstruction Model

Terahertz time domain spectroscopy imaging systems suffer from the problems of long image acquisition time and massive data processing. Reducing the sampling rate will lead to the degradation of the imaging reconstruction quality. To solve this issue, a novel terahertz imaging model, named the dual sparsity constraints terahertz image reconstruction model (DSC-THz), is proposed in this paper. DSC-THz fuses the sparsity constraints of the terahertz image in wavelet and gradient domains into the terahertz image reconstruction model. Differing from the conventional wavelet transform, we introduce a non-linear exponentiation transform into the shift invariant wavelet coefficients, which can amplify the significant coefficients and suppress the small ones. Simultaneously, the sparsity of the terahertz image in gradient domain is used to enhance the sparsity of the image, which has the advantage of edge preserving property. The split Bregman iteration scheme is utilized to tackle the optimization problem. By using the idea of separation of variables, the optimization problem is decomposed into subproblems to solve. Compared with the conventional single sparsity constraint terahertz image reconstruction model, the experiments verified that the proposed approach can achieve higher terahertz image reconstruction quality at low sampling rates.

CURVELET-WAVELET REGULARIZED SPLIT BREGMAN ITERATION FOR COMPRESSED SENSING

2011 ◽  
Vol 09 (01) ◽  
pp. 79-110 ◽  
Author(s):  
GERLIND PLONKA ◽  
JIANWEI MA
Keyword(s):  
Compressed Sensing ◽  
Optimization Problem ◽  
Constrained Optimization Problem ◽  
Split Bregman ◽  
Split Bregman Iteration ◽  
Special Cases ◽  
Sparsity Constraints ◽  
Iteration Methods ◽  
Wave Atoms ◽  
Sparsity Constrained Optimization

Compressed sensing is a new concept in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, compressed sensing allows one to recover this signal from much fewer samples than the Shannon–Nyquist theory requires. Many images can be sparsely approximated in expansions of suitable frames as wavelets, curvelets, wave atoms and others. Generally, wavelets represent point-like features while curvelets represent line-like features well. For a suitable recovery of images, we propose models that contain weighted sparsity constraints in two different frames. Given the incomplete measurements f = Φu + ϵ with the measurement matrix Φ ∈ ℝK × N, K ≪ N, we consider a jointly sparsity-constrained optimization problem of the form [Formula: see text]. Here Ψc and Ψw are the transform matrices corresponding to the two frames, and the diagonal matrices Λc, Λw contain the weights for the frame coefficients. We present efficient iteration methods to solve the optimization problem, based on Alternating Split Bregman algorithms. The convergence of the proposed iteration schemes will be proved by showing that they can be understood as special cases of the Douglas–Rachford Split algorithm. Numerical experiments for compressed sensing-based Fourier-domain random imaging show good performances of the proposed curvelet-wavelet regularized split Bregman (CWSpB) methods, where we particularly use a combination of wavelet and curvelet coefficients as sparsity constraints.

scholarly journals Detailed Analytical Approach to Solve the Magnetoacoustic Tomography with Magnetic Induction (MAT-MI) Problem for Three-Layer Objects

Energies ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 6515
Author(s):  
Adam Ryszard Zywica ◽  
Marcin Ziolkowski ◽  
Stanislaw Gratkowski
Keyword(s):  
Image Reconstruction ◽  
Magnetic Induction ◽  
Analytical Approach ◽  
Numerical Solutions ◽  
Separation Of Variables ◽  
Radiation Theory ◽  
Reconstruction Quality ◽  
Complex Shapes ◽  
Analytical Formulas ◽  
Analytical Expressions

This paper is devoted to an analytical approach to the magnetoacoustic tomography with magnetic induction (MAT-MI) problem for three-layer low-conductivity objects. For each layer, we determined closed-form analytical expressions for the eddy current density and Lorentz force vectors based on the separation of variables method. Next, the analytical formulas were validated with numerical solutions obtained with the help of the finite element method (FEM). Based on the acoustic dipole radiation theory, the influence of the transducer reception pattern on MAT-MI was investigated. To obtain acoustic wave patterns, as a system transfer function we proposed the Morlet wavelet. Finally, image reconstruction examples for objects of more complex shapes are presented, and the influence of the MAT-MI scanning resolution and the presence of the noise on the image reconstruction quality was studied in detail.

An Algorithm of Image Coding Based on Compressive Sensing

2013 ◽  
Vol 427-429 ◽  
pp. 1849-1852
Author(s):  
Dong Cheng Shi ◽  
Yi Dan Xing ◽  
Xiao Ding Shi
Keyword(s):  
Image Reconstruction ◽  
Compressive Sensing ◽  
Image Coding ◽  
Sampling Rate ◽  
Measurement Matrix ◽  
Block Algorithm ◽  
Optimum Parameters ◽  
Block Sizes ◽  
Reconstruction Model ◽  
Reconstruction Time

Block Compressive Sensing (BCS) is a image reconstruction model based on CS theory. By use the same measurement matrix to obtain the data in the form of Block × Block. Algorithm meaning to solve the problem that the traditional CS measurement matrix required for large storage, but different block has important influence on reconstruction time and effect. In this paper, find out the optimum parameters of the block. By compared the PSNR and reconstructed image effect under different sampling rate and different block sizes.

An ordered-subsets proximal preconditioned gradient algorithm for edge-preserving PET image reconstruction

2013 ◽  
Vol 40 (5) ◽  
pp. 052503 ◽  
Author(s):  
Abolfazl Mehranian ◽  
Arman Rahmim ◽  
Mohammad Reza Ay ◽  
Fotis Kotasidis ◽  
Habib Zaidi
Keyword(s):  
Image Reconstruction ◽  
Gradient Algorithm ◽  
Edge Preserving ◽  
Pet Image Reconstruction

Ultra-limited-angle CT image reconstruction algorithm based on reweighting and edge-preserving

2022 ◽  
pp. 1-13
Author(s):  
Lei Shi ◽  
Gangrong Qu ◽  
Yunsong Zhao
Keyword(s):  
Image Reconstruction ◽  
Condition Number ◽  
Reconstruction Algorithm ◽  
Projection Data ◽  
Ct Image ◽  
Reconstruction Algorithms ◽  
Edge Preserving ◽  
Image Reconstruction Algorithm ◽  
Ct Image Reconstruction ◽  
Limited Angle

BACKGROUND: Ultra-limited-angle image reconstruction problem with a limited-angle scanning range less than or equal to π 2 is severely ill-posed. Due to the considerably large condition number of a linear system for image reconstruction, it is extremely challenging to generate a valid reconstructed image by traditional iterative reconstruction algorithms. OBJECTIVE: To develop and test a valid ultra-limited-angle CT image reconstruction algorithm. METHODS: We propose a new optimized reconstruction model and Reweighted Alternating Edge-preserving Diffusion and Smoothing algorithm in which a reweighted method of improving the condition number is incorporated into the idea of AEDS image reconstruction algorithm. The AEDS algorithm utilizes the property of image sparsity to improve partially the results. In experiments, the different algorithms (the Pre-Landweber, AEDS algorithms and our algorithm) are used to reconstruct the Shepp-Logan phantom from the simulated projection data with noises and the flat object with a large ratio between length and width from the real projection data. PSNR and SSIM are used as the quantitative indices to evaluate quality of reconstructed images. RESULTS: Experiment results showed that for simulated projection data, our algorithm improves PSNR and SSIM from 22.46db to 39.38db and from 0.71 to 0.96, respectively. For real projection data, our algorithm yields the highest PSNR and SSIM of 30.89db and 0.88, which obtains a valid reconstructed result. CONCLUSIONS: Our algorithm successfully combines the merits of several image processing and reconstruction algorithms. Thus, our new algorithm outperforms significantly other two algorithms and is valid for ultra-limited-angle CT image reconstruction.

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