Two-step Iterative Shrinkage Thresholding Algorithm Research Articles

Learned Two-Step Iterative Shrinkage Thresholding Algorithm for Deep Compressive Sensing

Learned Two-Step Iterative Shrinkage Thresholding Algorithm for Deep Compressive Sensing

A Fast Intersection of Confidence Intervals Method-Based Adaptive Thresholding for Sparse Image Reconstruction Using the Matrix Form of the Wavelet Transform

One of the frequently used classes of sparse reconstruction algorithms is based on the iterative shrinkage/thresholding procedure, in which the thresholding parameter controls a trade-off between the algorithm’s accuracy and execution time. In order to avoid this trade-off, we propose using a fast intersection of confidence intervals method in order to adaptively control the threshold value throughout the iterations of the reconstruction algorithm. We have upgraded the two-step iterative shrinkage thresholding algorithm with a such procedure, improving its performance. The proposed algorithm, denoted as the FICI-TwIST, along with a few selected state-of-the-art sparse reconstruction algorithms, has been tested on the classical problem of image recovery by emphasizing the image sparsity in the discrete cosine and the discrete wavelet domain. Furthermore, we have derived a single wavelet transformation matrix which avoids wrapping effects, thereby achieving significantly faster execution times as compared to a more traditional function-based transformation. The obtained results indicate the competitive performance of the proposed algorithm, even in cases where all algorithm parameters have been individually fine-tuned for best performance.

Terahertz nondestructive stratigraphic reconstruction of paper stacks based on adaptive sparse deconvolution

Characterizing the number of sheets in a stack of paper typically involves mechanical separation of the individual sheets. Here, we explore an nondestructive method that can be applied to the intact paper stack. Namely, terahertz time-of-flight tomography, together with post signal-processing technique sparse deconvolution based on a two-step iterative shrinkage-thresholding algorithm (SD/TWIST), is employed to reconstruct the stratigraphy of stacks of sheets of paper with multilayered structure in a nondestructive and noncontact manner. The double-Gaussian mixture model (DGMM) is also incorporated to suppress dispersion in the reflected THz echoes. The effectiveness and accuracy of the proposed adaptive sparse-deconvolution method are verified experimentally and numerically. Compared with the commonly used frequency wavelet-domain deconvolution (FWDD) method and previous implementations of sparse deconvolution based on an iterative-shrinkage and thresholding algorithm (SD/IST), the proposed sparse-deconvolution approach can provide a clearer and rapid stratigraphic reconstruction of the paper stacks studied, while ensuring accurate thickness information for each paper sheet in the presence of noise, revealing the potential usage of real-time THz tomographic-image processing.

High precision reconstruction for compressed femtosecond dynamics images based on the TVAL3 algorithm

Compressed sensing (CS) has been successfully demonstrated to reconstruct ultrafast dynamic scenes in ultrafast imaging techniques with large sequence depth. Since compressed ultrafast imaging used a two-step iterative shrinkage/thresholding (TwIST) algorithm in previous image reconstruction, some details of the object will not be recovered when the amount of data compression is large. Here we applied a more efficient Total Variation (TV) minimization scheme based on augmented Lagrangian and alternating direction algorithms (TVAL3) to reconstruct the ultrafast process. In order to verify the effectiveness of the TVAL3 algorithm, we experimentally compare the reconstruction quality of TVAL3 algorithm and TwIST algorithm in an ultrafast imaging system based on compressed-sensing and spectral-temporal coupling active detection with highest frame rate of 4.37 trillion Hz. Both dynamic and static experimental results show that, TVAL3 algorithm can not only reconstruct a rapidly moving light pulse with a more precise profile and more fitted trajectory, but also improve the quality of static objects and the speed of reconstruction. This work will advance the ultrafast imaging techniques based on compressed sensing in terms of image reconstruction quality and reconstruction speed, which finally helps promoting the application of these techniques in areas where high spatial precision is required, such as phase transitions and laser filamentation in nonlinear solids, etc.

Sparse reconstruction of magnetic resonance image combined with two-step iteration and adaptive shrinkage factor.

As an advanced technique, compressed sensing has been used for rapid magnetic resonance imaging in recent years, Two-step Iterative Shrinkage Thresholding Algorithm (TwIST) is a popular algorithm based on Iterative Thresholding Shrinkage Algorithm (ISTA) for fast MR image reconstruction. However TwIST algorithms cannot dynamically adjust shrinkage factor according to the degree of convergence. So it is difficult to balance speed and efficiency. In this paper, we proposed an algorithm which can dynamically adjust the shrinkage factor to rebalance the fidelity item and regular item during TwIST iterative process. The shrinkage factor adjusting is judged by the previous reconstructed results throughout the iteration cycle. It can greatly accelerate the iterative convergence while ensuring convergence accuracy. We used MR images with 2 body parts and different sampling rates to simulate, the results proved that the proposed algorithm have a faster convergence rate and better reconstruction performance. We also used 60 MR images of different body parts for further simulation, and the results proved the universal superiority of the proposed algorithm.

TwIST sparse regularization method using cubic B-spline dual scaling functions for impact force identification

For impact force identification, as a severe ill-posed inverse problem, the wavelet-transform method individually requires a large and accurate decomposition level to obtain a robust and accurate result. However, continuing to increase the number of cubic B-spline dual scaling functions will make the cost of calculation too expansive. To overcome the above mentioned difficulties of impact force identification, sparse regularization is used as a post-processing to solve the residual ill-posed problems. During the iteration process of sparse regularization, the two-step iterative shrinkage-thresholding algorithm (TwIST) algorithm is applied rather than the original iterative shrinkage-thresholding (IST) algorithm, which is more suitable for sparse solution. By combining cubic B-spline scaling functions as pre-processing and TwIST sparse regularization algorithm as post-processing, the proposed method TwIST-SpaR-CB can obtain better impact force identification accuracy with improved computational efficiency. The effectiveness and accuracy of the proposed method compared with the two individual method were verified by experimental and numerical results.

Study on the length of diagnostic time window of CUP-VISAR

One-dimensional line velocity interferometer system for any reflectors (VISARs) acts as a significant diagnostic device in the process of the inertial confinement fusion, which can be used to measure the free surface velocity and the history of shockwave velocity in transparent media over time. But the lack of spatial information makes it impossible to measure the flatness of wavefront. The compressed ultrafast photography (CUP) system developed in recent years can realize two-dimensional ultrafast photography. We have designed a new two-dimensional VISAR diagnosis system by combining the CUP with line-VISAR, called the CUP-VISAR, which will be of great significance in two-dimensional shockwave front measurement. In this paper, a data simulation method of CUP-VISAR is proposed to study the length of diagnostic time window of the device. A series of original VIASR images are firstly generated and then the compressed images are simulated after image encoding and compression. Finally, two-step iterative shrinkage thresholding algorithm is used to reconstruct the compressed images, which results in corresponding reconstructed images. In order to verify the restoration effect of the algorithm, we calculate the velocity error and image correlation coefficient value. Finally the relationship between the image reconstruction quality and the number of images is preliminarily obtained, which provides reference for the actual experiment.

Honeycomb pattern removal for fiber bundle endomicroscopy based on a two-step iterative shrinkage thresholding algorithm

Fiber bundle endomicroscopy has potential for facilitating high-resolution (HR) in vivo imaging. One of the main challenges of this technique is the improvement of image restoration for better visualization. In this paper, we propose to reconstruct a HR image without a fixed honeycomb pattern from a noisy observation image, which can be formulated as an inverse problem. We use the obtained fixed honeycomb pattern as a prior image and use a two-step iterative shrinkage thresholding algorithm with a total variation regularization to solve this problem. In addition to the fixed honeycomb pattern removal, our method can also improve spatial resolution. The feasibility of our method is demonstrated by the images obtained from the USAF target and spider silks. In each ease, our method recovers more details than that recovered by the conventional method. The proposed theoretical framework for the removal of the honeycomb pattern in this paper shows promising and wide applications for fiber bundle imaging.

Improving the image reconstruction quality of compressed ultrafast photography via an augmented Lagrangian algorithm

Compressed ultrafast photography (CUP) has been shown to be a powerful tool to measure ultrafast dynamic scenes. In previous studies, CUP used a two-step iterative shrinkage/thresholding (TwIST) algorithm to reconstruct three-dimensional image information. However, the image reconstruction quality greatly depended on the selection of the penalty parameter, which caused the reconstructed images to be unable to be correctly determined if the ultrafast dynamic scenes were unknown in advance. Here, we develop an augmented Lagrangian (AL) algorithm for the image reconstruction of CUP to overcome the limitation of the TwIST algorithm. Our numerical simulations and experimental results show that, compared to the TwIST algorithm, the AL algorithm is less dependent on the selection of the penalty parameter, and can obtain higher image reconstruction quality. This study solves the problem of the image reconstruction instability, which may further promote the practical applications of CUP.

Sparse time–frequency distributions based on the $$\ell _1$$ ℓ 1 -norm minimization with the fast intersection of confidence intervals rule

Methods based on the sparsity constraint have been recently introduced to the time–frequency (TF) signal processing, achieving artifact suppression by exploiting the fact that most real-life signals are sparse in the TF domain. In this paper, we propose a sparse reconstruction algorithm based on the two-step iterative shrinkage/thresholding (TwIST) algorithm. In the proposed TwIST algorithm modification, the soft-thresholding value is adaptively determined by the fast intersection of the confidence intervals (FICI) rule in each iteration of the reconstruction algorithm. The FICI rule is used to determine the TF region with the lowest mean value, and the soft-thresholding value is set to the largest sample value inside the region. The performance of the proposed algorithm has been compared to the performance of the state-of-the-art reconstruction algorithms in terms of their execution time and concentration of the resulting TF distribution.

A Robust Algorithm for 2-D NMR Diffusion–Relaxation Spectra Inversion

A two-step iterative shrinkage/thresholding (TIST) algorithm was proposed to solve the objective function of the L1 regularization for the 2-D nuclear magnetic resonance diffusion–relaxation ( $D - T_{2}$ ) spectra inversion. Moreover, a simple and effective method combining the S-curve method and the Chi-square method was proposed to select the optimal L1 regularization parameter. We compared the inverted $D - T_{2}$ spectra derived from the TIST algorithm with those from the truncated singular value decomposition (TSVD), Butler–Reeds–Dawson (BRD), original IST (OIST), and IST algorithms using numerical experiments. The experimental results indicated that the inverted $D - T_{2}$ spectra derived from the OIST, IST, and TIST algorithms were affected by noise to a smaller degree, and the robustness was higher for the OIST, IST, and TIST algorithms than for the TSVD and BRD algorithms. In addition, we compared the accuracy and operating time of the TIST, OIST, and IST algorithms for $D - T_{2}$ spectra inversion and concluded that the three algorithms had an equivalent accuracy but the TIST algorithm had a faster convergence rate.

Speech Signal Reconstruction using Two-Step Iterative Shrinkage Thresholding Algorithm

Speech Signal Reconstruction using Two-Step Iterative Shrinkage Thresholding Algorithm

Sparse-View CT Image Recovery Using Two-Step Iterative Shrinkage-Thresholding Algorithm

We investigate an image recovery method for sparse-view computed tomography (CT) using an iterative shrinkage algorithm based on a second-order approach. The two-step iterative shrinkage-thresholding (TwIST) algorithm including a total variation regularization technique is elucidated to be more robust than other first-order methods; it enables a perfect restoration of an original image even if given only a few projection views of a parallel-beam geometry. We find that the incoherency of a projection system matrix in CT geometry sufficiently satisfies the exact reconstruction principle even when the matrix itself has a large condition number. Image reconstruction from fan-beam CT can be well carried out, but the retrieval performance is very low when compared to a parallel-beam geometry. This is considered to be due to the matrix complexity of the projection geometry. We also evaluate the image retrieval performance of the TwIST algorithm using measured projection data.

Multiple-image encryption based on compressive holography using a multiple-beam interferometer

Multiple-image encryption techniques not only improve the encryption capacity but also facilitate the transmission and storage of the ciphertext. We present a new method of multiple-image encryption based on compressive holography with enhanced data security using a multiple-beam interferometer. By modifying the Mach–Zehnder interferometer, the interference of multiple object beams and unique reference beam is implemented for encrypting multiple images simultaneously into one hologram. The original images modulated with the random phase masks are put in different positions with different distance away from the CCD camera. Each image plays the role of secret key for other images to realize the mutual encryption. Four-step phase shifting technique is combined with the holographic recording. The holographic recording is treated as a compressive sensing process, thus the decryption process is inverted as a minimization problem and the two-step iterative shrinkage/thresholding algorithm (TwIST) is employed to solve this optimization problem. The simulated results about multiple binary and grayscale images encryption are demonstrated to verify the validity and robustness of our proposed method.