Coded aperture compressive temporal imaging via unsupervised lightweight local-global networks with geometric characteristics.

Coded aperture compressive temporal imaging (CACTI) utilizes compressive sensing (CS) theory to compress three dimensional (3D) signals into 2D measurements for sampling in a single snapshot measurement, which in turn acquires high-dimensional (HD) visual signals. To solve the problems of low quality and slow runtime often encountered in reconstruction, deep learning has become the mainstream for signal reconstruction and has shown superior performance. Currently, however, impressive networks are typically supervised networks with large-sized models and require vast training sets that can be difficult to obtain or expensive. This limits their application in real optical imaging systems. In this paper, we propose a lightweight reconstruction network that recovers HD signals only from compressed measurements with noise and design a block consisting of convolution to extract and fuse local and global features, stacking multiple features to form a lightweight architecture. In addition, we also obtain unsupervised loss functions based on the geometric characteristics of the signal to guarantee the powerful generalization capability of the network in order to approximate the reconstruction process of real optical systems. Experimental results show that our proposed network significantly reduces the model size and not only has high performance in recovering dynamic scenes, but the unsupervised video reconstruction network can approximate its supervised version in terms of reconstruction performance.

Coded aperture compression temporal imaging based on a dual-mask and deep denoiser.

Coded aperture compressive temporal imaging (CACTI) is the mapping of multiple frames using different encoding patterns into a single measurement and then using an algorithm to reconstruct the required high-dimensional signals, thus enabling high-speed photography on low-speed cameras. An encoding pattern and a reconstruction algorithm both play a critical role for CACTI. To improve the quality of the reconstruction, in terms of encoding, we took advantage of the reflective properties of the digital micromirror device and used a complementary dual-mask pattern to obtain more projection information. In terms of decoding, we developed what we believe, to the best of our knowledge, is a new model combining the weighted Landweber regularization with the relaxation strategy and a deep denoiser. The experimental results show the superiority of our proposed encoding-decoding combination, which achieves better performance in terms of the peak SNR, structural similarity index measure, and visual effects.

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

BACKGROUND: Ultra-limited-angle image reconstruction problem with a limited-angle scanning range less than or equal to π2 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.

A preconditioned landweber iteration scheme for the limited-angle image reconstruction.

BACKGROUND: The limited-angle reconstruction problem is of both theoretical and practical importance. Due to the severe ill-posedness of the problem, it is very challenging to get a valid reconstructed result from the known small limited-angle projection data. The theoretical ill-posedness leads the normal equation AT Ax = AT b of the linear system derived by discretizing the Radon transform to be severely ill-posed, which is quantified as the large condition number of AT A. OBJECTIVE: To develop and test a new valid algorithm for improving the limited-angle image reconstruction with the known appropriately small angle range from [0,π3]∼[0,π2]. METHODS: We propose a reweighted method of improving the condition number of AT Ax = AT b and the corresponding preconditioned Landweber iteration scheme. The weight means multiplying AT Ax = AT b by a matrix related to AT A, and the weighting process is repeated multiple times. In the experiment, the condition number of the coefficient matrix in the reweighted linear system decreases monotonically to 1 as the weighting times approaches infinity. RESULTS: The numerical experiments showed that the proposed algorithm is significantly superior to other iterative algorithms (Landweber, Cimmino, NWL-a and AEDS) and can reconstruct a valid image from the known appropriately small angle range. CONCLUSIONS: The proposed algorithm is effective for the limited-angle reconstruction problem with the known appropriately small angle range.

Accelerated strategy for the MLEM algorithm.

BACKGROUND: A statistical method called maximum likelihood expectation maximization (MLEM) is quite attractive, especially in PET/SPECT. However, the convergence rate of the iterative scheme of MLEM is quite slow. OBJECTIVE: This study aims to develop and test a new method to speed up the convergence rate of the MLEM algorithm. METHODS: We introduce a relaxation parameter in the conventional MLEM iterative formula and propose the relaxation strategy on the condition that the spectral radius of the derived iterative matrix from the iterative scheme with the accelerated parameter reaches a minimum value. RESULTS: Experiments with Shepp-Logan phantom and an annual tree image demonstrate that the new computational strategy effectively accelerates computation time while maintains reasonable image quality. CONCLUSIONS: The proposed new computational method involving the relaxation strategy has a faster convergence speed than the original method.

Combine TV-L1 model with guided image filtering for wide and faint ring artifacts correction of in-line x-ray phase contrast computed tomography.

In practice, mis-calibrated detector pixels give rise to wide and faint ring artifacts in the reconstruction image of the In-line phase-contrast computed tomography (IL-PC-CT). Ring artifacts correction is essential in IL-PC-CT. In this study, a novel method of wide and faint ring artifacts correction was presented based on combining TV-L1 model with guided image filtering (GIF) in the reconstruction image domain. The new correction method includes two main steps namely, the GIF step and the TV-L1 step. To validate the performance of this method, simulation data and real experimental synchrotron data are provided. The results demonstrate that TV-L1 model with GIF step can effectively correct the wide and faint ring artifacts for IL-PC-CT.

Simultaneous algebraic reconstruction technique based on guided image filtering.

The challenge of computed tomography is to reconstruct high-quality images from few-view projections. Using a prior guidance image, guided image filtering smoothes images while preserving edge features. The prior guidance image can be incorporated into the image reconstruction process to improve image quality. We propose a new simultaneous algebraic reconstruction technique based on guided image filtering. Specifically, the prior guidance image is updated in the image reconstruction process, merging information iteratively. To validate the algorithm practicality and efficiency, experiments were performed with numerical phantom projection data and real projection data. The results demonstrate that the proposed method is effective and efficient for nondestructive testing and rock mechanics.

Necessary and sufficient convergence conditions for algebraic image reconstruction algorithms.

The Landweber scheme is an algebraic reconstruction method and includes several important algorithms as its special cases. The convergence of the Landweber scheme is of both theoretical and practical importance. Using the singular value decomposition (SVD), we derive an iterative representation formula for the Landweber scheme and consequently establish the necessary and sufficient conditions for its convergence. In addition to verifying the necessity and sufficiency of known convergent conditions, we find new convergence conditions allowing relaxation coefficients in an interval not covered by known results. Moreover, it is found that the Landweber scheme can converge within finite iterations when the relaxation coefficients are chosen to be the inverses of squares of the nonzero singular values. Furthermore, the limits of the Landweber scheme in all convergence cases are shown to be the sum of the minimum norm solution of a weighted least-squares problem and an oblique projection of the initial image onto the null space of the system matrix.