Two-step Iterative Shrinkage/thresholding Research Articles

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

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

Brain Stroke Detection Using Machine Learning

Abstract: We look at the skills of metamaterials technology to enhance the first-rate of reconstructed photos for the hassle of mind stroke detection. We combine the metamaterial in our headscarf system for mind imaging in CST, and evaluate the reconstructed pix of the pinnacle model this is positioned in the microwave tomographic head machine for the cases with and with out the incorporated metamaterial. For photograph reconstruction we observe the distorted Born iterative technique (DBIM) mixed with two-step iterative shrinkage/thresholding (TwIST) set of rules. Our consequences imply that using our metamaterial can increase the signal distinction due to the presence of a blood goal, which translates into more ac- curate reconstructions of the target.

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.

URBAN 3D RECONSTRUCTION OF VHR SAR IMAGES USING ITERATIVE OPTIMIZATION ALGORITHM AND LAYOVER FIXED-ORDER MODEL

Abstract. Synthetic Aperture Radar (SAR) Tomography (TomoSAR) is a three-dimensional SAR imaging technique that uses multiple passes to process complex SAR images and obtain three-dimensional spatial scattering information to derive the elevation scattering distribution. Due to its own shortcomings, the elevation obtained by the traditional spectral estimation method has low resolution in the elevation direction and is affected by noise. The imaging algorithm based on compressed sensing can achieve super-resolution reconstruction in the elevation direction while reducing the number of observations. However, the CS algorithm still faces challenges when applied to real-world tomographic SAR imaging. In particular, it often requires numerous iterations to achieve satisfactory results, which significantly reduces its processing efficiency in large-scale tomography. To address the above issues, in this paper, we proposed an urban 3D reconstruction of VHR SAR images using an iterative optimization algorithm and layover fixed-order model. The iterative optimization algorithm and the layover fixed-order model consist of two parts: The TomoSAR imaging equation is solved by the two-step iterative shrinkage/thresholding (TwIST) algorithm, and the number of scatterers K is estimated by the Bayesian Information Criterion (BIC). In this paper, the effectiveness of TwIST-BIC in TomoSAR imaging in urban areas is verified with real TerraSARX data. By comparing with the OMP algorithm based on matching tracking and the FISTA algorithm based on gradient descent. The TWIST-BIC method is less complex, converges faster, and combines both execution speed and super-resolution, which can effectively solve the processing efficiency problem in large-area tomography and acquire high-resolution tomographic analysis.

Frequency-domain compression imaging for extending the field of view of infrared thermometers.

We propose a computational imaging technique for expanding the field of view of infrared thermometers. The contradiction between the field of view and the focal length has always been a chief problem for researchers, especially in infrared optical systems. Large-area infrared detectors are expensive and technically arduous to be manufactured, which enormously limits the performance of the infrared optical system. On the other hand, the extensive use of infrared thermometers in COVID-19 has created a considerable demand for infrared optical systems. Therefore, improving the performance of infrared optical systems and increasing the utilization of infrared detectors is vital. This work proposes a multi-channel frequency-domain compression imaging method based on point spread function (PSF) engineering. Compared with conventional compressed sensing, the submitted method images once without an intermediate image plane. Furthermore, phase encoding is used without loss of illumination of the image surface. These facts can significantly reduce the volume of the optical system and improve the energy efficiency of the compressed imaging system. Therefore, its application in COVID-19 is of great value. We design a dual-channel frequency-domain compression imaging system to verify the proposed method's feasibility. Then, the wavefront coded PSF and optical transfer function (OTF) are used, and the two-step iterative shrinkage/thresholding (TWIST) algorithm is used to restore the image to get the final result. This compression imaging method provides a new idea for the large field of view monitoring systems, especially in infrared optical systems.

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.

Experimental Validation of the DBIM-TwIST Algorithm for Brain Stroke Detection and Differentiation Using a Multi-Layered Anatomically Complex Head Phantom

We present an experimental validation of the distorted Born iterative method with the two-step iterative shrinkage thresholding (DBIM-TwIST) algorithm for the problem of brain stroke detection and differentiation, using an anatomically accurate, multi-layer head phantom. To this end, we have developed a gelatine-based, anatomically complex head phantom which mimics various brain tissues and also includes a target mimicking hemorrhagic or ischemic stroke. We simulated the model and setup using CST Microwave Studio and then used our experimental imaging setup to collect numerical and measured data, respectively. We then used our DBIM-TwIST algorithm to reconstruct the dielectric properties of the imaging domain for both simulated and measured data. Results from our CST simulations showed that we are able to locate and reconstruct the permittivity of different stroke targets using an approximate initial guess. Our experimental results demonstrated the potential and challenges for successful detection and differentiation of the stroke targets.

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.

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.

High-fidelity image reconstruction for compressed ultrafast photography via an augmented-Lagrangian and deep-learning hybrid algorithm

Compressed ultrafast photography (CUP) is the fastest single-shot passive ultrafast optical imaging technique, which has shown to be a powerful tool in recording self-luminous or non-repeatable ultrafast phenomena. However, the low fidelity of image reconstruction based on the conventional augmented-Lagrangian (AL) and two-step iterative shrinkage/thresholding (TwIST) algorithms greatly prevents practical applications of CUP, especially for those ultrafast phenomena that need high spatial resolution. Here, we develop a novel AL and deep-learning (DL) hybrid (i.e., AL + DL ) algorithm to realize high-fidelity image reconstruction for CUP. The AL + DL algorithm not only optimizes the sparse domain and relevant iteration parameters via learning the dataset but also simplifies the mathematical architecture, so it greatly improves the image reconstruction accuracy. Our theoretical simulation and experimental results validate the superior performance of the AL + DL algorithm in image fidelity over conventional AL and TwIST algorithms, where the peak signal-to-noise ratio and structural similarity index can be increased at least by 4 dB (9 dB) and 0.1 (0.05) for a complex (simple) dynamic scene, respectively. This study can promote the applications of CUP in related fields, and it will also enable a new strategy for recovering high-dimensional signals from low-dimensional detection.

Minimum Redundancy Array—A Baseline Optimization Strategy for Urban SAR Tomography

Synthetic aperture radar (SAR) tomography (TomoSAR) is able to separate multiple scatterers layovered inside the same resolution cell in high-resolution SAR images of urban scenarios, usually with a large number of orbits, making it an expensive and unfeasible task for many practical applications. Targeting at finding out the minimum number of images necessary for tomographic reconstruction, this paper innovatively applies minimum redundancy array (MRA) for tomographic baseline array optimization. Monte Carlo simulations are conducted by means of Two-step Iterative Shrinkage/Thresholding (TWIST) and Truncated Singular Value Decomposition (TSVD) to fully evaluate the tomographic performance of MRA orbits in terms of detection rates, Cramer Rao Lower Bounds, as well as resistance against sidelobes. Experiments on COSMO-SkyMed and TerraSAR-X/TanDEM-X data are also conducted in this paper. The results from simulations and experiments on real data have both demonstrated that introducing MRA for baseline optimization in SAR tomography can benefit from the dramatic reduction of necessary orbit numbers, if the recently proposed TWIST method is used for tomographic reconstruction. Although the simulation and experiments in this manuscript are carried out using spaceborne data, the outcome of this paper can also give examples for airborne TomoSAR when designing flight orbits using airborne sensors.

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.

Experimental Validation of Microwave Tomographywith the DBIM-TwIST Algorithm for Brain StrokeDetection and Classification.

We present an initial experimental validation of a microwave tomography (MWT) prototype for brain stroke detection and classification using the distorted Born iterative method, two-step iterative shrinkage thresholding (DBIM-TwIST) algorithm. The validation study consists of first preparing and characterizing gel phantoms which mimic the structure and the dielectric properties of a simplified brain model with a haemorrhagic or ischemic stroke target. Then, we measure the S-parameters of the phantoms in our experimental prototype and process the scattered signals from 0.5 to 2.5 GHz using the DBIM-TwIST algorithm to estimate the dielectric properties of the reconstruction domain. Our results demonstrate that we are able to detect the stroke target in scenarios where the initial guess of the inverse problem is only an approximation of the true experimental phantom. Moreover, the prototype can differentiate between haemorrhagic and ischemic strokes based on the estimation of their dielectric properties.

Single-shot optical multiple-image encryption by jointly using wavelength multiplexing and position multiplexing.

A single shot large-capacity optical multiple-image encryption method based on wavelength multiplexing and position multiplexing is proposed. In the encryption process of the proposed method, multiple plane waves of different wavelengths are adopted to illuminate secret images that are placed at different positions along the optical axis. All the secret images are encoded into a single grayscale intensity-only image that is recorded by a monochromic camera by applying a diffractive-imaging based double random phase encoding (DRPE) system. In the decryption process, high accuracy images are decrypted without crosstalk from the intensity image through a multimode phase retrieval algorithm and a two-step iterative shrinkage/thresholding (TwIST) algorithm. The feasibility of the proposed method is demonstrated by numerical simulations.

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.

Development of energy correction based multishot snapshot spectral imaging system

Abstract Spectrum of light reflected from an object is a fingerprint of its physical and chemical properties. In this paper, we proposed an energy correction based coded aperture snapshot spectral imaging (EC-CASSI) system to obtain the spatial/spectral data cube reflected from the object scene. Coded aperture was specifically designed in the system to efficiently compress input data in one shot. Based on the Two-step Iterative Shrinkage Thresholding (TwIST) algorithm, EC-TwIST was proposed with two-step energy correction to achieve higher accuracy in hyperspectral imaging reconstruction. Results showed that spatiospectral cube acquisition accuracy of EC-CASSI were 34.78% (differential relative spectral quadratic error evaluation) and 89.71% (entropy bias evaluation) higher than traditional CASSI system, respectively. This highly computation-relied spectrum obtainment method showed great potential in the application of machine vision and auto recognition.

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.