Super-resolution photoacoustic imaging of sparse absorbers using L1-norm minimization (Conference Presentation)

In this chapter, the authors propose a Super-Resolution (SR) method using a vector quantization codebook and filter dictionary. In the process of SR, we use the idea of compressive sensing to represent a sparsely sampled signal under the assumption that a combination of a small number of codewords can represent an image patch. A low-resolution image is obtained from an original high-resolution image, degraded by blurring and down-sampling. The authors propose a resolution enhancement using an alternative l1 norm minimization to overcome the convexity of l0 norm and the sparsity of l1 norm at the same time, where an iterative reweighted l1 norm minimization is used for optimization. After the reconstruction stage, because the optimization is implemented on image patch basis, an additional deblurring or denoising step is used to globally enhance the image quality. Experiment results show that the proposed SR method provides highly efficient results.

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A Photoacoustic Imaging Algorithm Based on Regularized Smoothed L0 Norm Minimization

Molecular Imaging ◽

10.1155/2021/6689194 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Xueyan Liu ◽

Limei Zhang ◽

Yining Zhang ◽

Lishan Qiao

Keyword(s):

Image Reconstruction ◽

Photoacoustic Imaging ◽

Sparse Sampling ◽

Signal Recovery ◽

L1 Norm ◽

High Quality ◽

Norm Minimization ◽

Reconstruction Quality ◽

Noisy Measurement ◽

Better Than

The recently emerging technique of sparse reconstruction has received much attention in the field of photoacoustic imaging (PAI). Compressed sensing (CS) has large potential in efficiently reconstructing high-quality PAI images with sparse sampling signal. In this article, we propose a CS-based error-tolerant regularized smooth L0 (ReSL0) algorithm for PAI image reconstruction, which has the same computational advantages as the SL0 algorithm while having a higher degree of immunity to inaccuracy caused by noise. In order to evaluate the performance of the ReSL0 algorithm, we reconstruct the simulated dataset obtained from three phantoms. In addition, a real experimental dataset from agar phantom is also used to verify the effectiveness of the ReSL0 algorithm. Compared to three L0 norm, L1 norm, and TV norm-based CS algorithms for signal recovery and image reconstruction, experiments demonstrated that the ReSL0 algorithm provides a good balance between the quality and efficiency of reconstructions. Furthermore, the PSNR of the reconstructed image calculated by the introduced method was better than the other three methods. In particular, it can notably improve reconstruction quality in the case of noisy measurement.

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Mixed lp/l1 Norm Minimization Approach to Intra-Frame Super-Resolution

IEICE Transactions on Information and Systems ◽

10.1587/transinf.2014edl8086 ◽

2014 ◽

Vol E97.D (10) ◽

pp. 2814-2817 ◽

Cited By ~ 2

Author(s):

Kazuma SHIMADA ◽

Katsumi KONISHI ◽

Kazunori URUMA ◽

Tomohiro TAKAHASHI ◽

Toshihiro FURUKAWA

Keyword(s):

Super Resolution ◽

L1 Norm ◽

Norm Minimization ◽

Minimization Approach

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Total Variation (TV) l1 Norm Minimization Based Limited Data X-ray CT Image Reconstruction

Research in Nondestructive Evaluation ◽

10.1080/09349847.2019.1673857 ◽

2019 ◽

Vol 31 (3) ◽

pp. 164-186 ◽

Cited By ~ 1

Author(s):

Shubhabrata Sarkar ◽

Pankaj Wahi ◽

Prabhat Munshi

Keyword(s):

Image Reconstruction ◽

Total Variation ◽

Ct Image ◽

Limited Data ◽

L1 Norm ◽

X Ray ◽

Norm Minimization ◽

Ct Image Reconstruction

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Accelerated 3D blind separation of convolved mixtures based on the fast iterative shrinkage thresholding algorithm for adaptive multiple subtraction

Geophysics ◽

10.1190/geo2016-0384.1 ◽

2018 ◽

Vol 83 (2) ◽

pp. V99-V113 ◽

Cited By ~ 7

Author(s):

Zhong-Xiao Li ◽

Zhen-Chun Li

Keyword(s):

Field Data ◽

Optimization Problem ◽

Computational Cost ◽

Computation Time ◽

Blind Separation ◽

L1 Norm ◽

Norm Minimization ◽

Iterative Shrinkage ◽

Thresholding Algorithm ◽

Iterative Shrinkage Thresholding

After multiple prediction, adaptive multiple subtraction is essential for the success of multiple removal. The 3D blind separation of convolved mixtures (3D BSCM) method, which is effective in conducting adaptive multiple subtraction, needs to solve an optimization problem containing L1-norm minimization constraints on primaries by the iterative reweighted least-squares (IRLS) algorithm. The 3D BSCM method can better separate primaries and multiples than the 1D/2D BSCM method and the method with energy minimization constraints on primaries. However, the 3D BSCM method has high computational cost because the IRLS algorithm achieves nonquadratic optimization with an LS optimization problem solved in each iteration. In general, it is good to have a faster 3D BSCM method. To improve the adaptability of field data processing, the fast iterative shrinkage thresholding algorithm (FISTA) is introduced into the 3D BSCM method. The proximity operator of FISTA can solve the L1-norm minimization problem efficiently. We demonstrate that our FISTA-based 3D BSCM method achieves similar accuracy of estimating primaries as that of the reference IRLS-based 3D BSCM method. Furthermore, our FISTA-based 3D BSCM method reduces computation time by approximately 60% compared with the reference IRLS-based 3D BSCM method in the synthetic and field data examples.

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