Evaluation on Compressive Sensing-based Image Reconstruction Method for Microwave Imaging

This paper demonstrates the merits of nested Compressive Sensing (CS) approach for Electrocardiogram (ECG) signals using discrete wavelet transform (DWT) and discrete cosine transform (DCT) as sensing matrix and sparsifying matrix. The implementation of CS framework is done using Gradient Projection for Sparse Reconstruction (GPSR). It is tested on 9 ECG signals of different arrhythmia categories obtained from MITBIH and BIDMC dataset. It is analysed for 3 different combinations, case (1) DCT sensing and DWT sparsification, case (2) DWT sensing and DCT sparsification and case (3) DWT sensing and DWT sparsification. A novel hybrid nested CS approach is proposed as case (4) which is a combination of case (2) in higher level and case (1) in lower level. This nested method yields the best PRD of 1.39 for CR = 0.2 and performs better than all proposed cases. This proposed approach involves a fair method of discarding the measurements in all frequency band and performs better than the state of the art work when the sampling rate is reduced by 4 times for ECG signal 100.dat from MIT-BIH (Massachusetts Institute of Technology-Beth Israel Hospital) database for CR = 0.2. It is shown that the reconstruction time of the proposed nested CS approach is lesser than non-nested CS approach.

This paper investigates a new multifrequency compressed sensing (CS) model for 2-D near-field microwave and millimeter-wave synthetic aperture radar (SAR) imaging system, which usually collects multifrequency sparse data. Spatial data of each frequency are represented as a hierarchical tree structure under a wavelet basis and spatial data of different frequencies are modeled as a joint structure, because they are highly correlated. Based on the developed multifrequency CS model, a new CS approach is proposed by exploiting both the intrafrequency and interfrequency correlations, and enriches the existing CS approaches for 2-D near-field microwave and millimeter-wave SAR image reconstruction from undersampled measurements. Combining a splitting Bregman update with a variation of the parallel Fast Iterative Shrinkage-Thresholding Algorithm-like proximal algorithm, the proposed CS approach minimizes a linear combination of five terms: a least squares data fitting, a $\textrm {multi-}\ell _{1}$ norm, a multitotal variation norm, a joint-sparsity $\ell _{21}$ norm, and a tree-sparsity overlapping $\ell _{21}$ norm. Simulation and experimental results demonstrate the superior performance of the proposed approach in terms of both efficiency and convergence speed.

Compressive sensing (CS) is a new technique that give an approach to reconstruct the signal with few numbers of observations or measurements. The CS is based on L1 -norm minimizations to find the sparse solutions and it is known as basis pursuit. In this investigation, CS scheme with different transforms is proposed. The three utilized transform techniques are: Discrete Fourier Transform(DFT), Discrete Cosine Transform(DCT) and Discrete Wavelet Transform(DWT) with daubechies1(DB1) and coiflets1(coif1) basis. The proposed system is tested by employing the following signals: Blocks, Heavy Sine, ‘Bumps’ and ‘Doppler’ which cover wide range of applications. The four testing signals are represented in sparse domain using different transforms. In order to threshold the coefficients of the signals in sparse domain, the universal threshold is utilized in the case of CS with FFT and DWT whereas, the universal threshold is modified to prune the DCT coefficients. The main aim of this study is to investigate the differences among CS with DFT, CS with DCT and CS with DWT, and consequently a suitable transform domain used with CS to be selected. The comparative study is established by assessing the performance of the proposed system using Root Mean Square Error (RMSE), output SNR, and the time required to reconstruct approximated signals. Simulation results have shown that the CS with DWT outperforms the CS with FFT and DCT. CS with DWT has achieved good RMSE values about (0.0014 to 3.359e-8) even when half of the signal elements are removed. CS with FFT and DCT enhanced the noisy Blocks and Bumps signals by 3dB and 1dB respectively, while it is failed to enhance noisy Heavy Sine and Doppler signals. CS with DWT of two basis and for single decomposition level have improved the noisy Blocks, Bumps, Heavy Sine and Doppler signals by 5dB, 4dB, 3dB, and 3dB respectively.

Reconstruction of atomic force microscopy image using compressed sensing

To develop a phase encoding reduction scheme based on compressed sensing (CS) for phase-encoded (1) H MR spectroscopic imaging (MRSI). Phantom and in vivo rat brain MRSI experiments were performed at 7 Tesla to examine the performance of CS approach and compare it with the full k-space acquisition. The CS undersampling was performed by acquiring a pseudorandom and density-varying subset of phase encodings. Residual water resonance was first removed from the undersampled k-space dataset before CS reconstruction. The CS reconstruction was performed by a linearized Bregman iteration procedure for efficiency in computing large scale L1 minimization. The spectral and spatial fidelity was evaluated by comparing spectral linewidths and metabolite maps and voxel-wise Bland-Altman analysis. CS preserved the spectral resolution and metabolite content levels. No spectral broadening was observed, and the estimation biases of the metabolite content levels were no more than 4%. CS clearly preserved the boundaries of metabolite maps but led to slight loss of details in metabolite maps. This study demonstrated the feasibility of the proposed CS approach to accelerate phase-encoded (1) H MRSI.

Compressive sensing (CS) idea enables the reconstruction of a sparse signal from a small set of measurements. CS approach has applications in many practical areas. One of the areas is radar systems. In this article, the radar ambiguity function is denoised within the CS framework. A new denoising method on the projection onto the epigraph set of the convex function is also developed for this purpose. This approach is compared to the other CS reconstruction algorithms. Experimental results are presented1.

A new compressed sensing (CS) image reconstruction method is proposed for high‐resolution wideband three‐dimensional synthetic aperture radar (SAR) imaging systems. In contrast to existing CS SAR methods that employ only a forward SAR transform in pre‐ or post‐processing, the proposed method employs both forward SAR and reverse SAR (R‐SAR) transforms in each CS iteration to improve the quality of reconstructed images. This study proposes a simple and elegant truncation repair method to combat the truncation error and utilises non‐uniform fast Fourier transform to reduce the SAR and R‐SAR transform errors, thereby ensuring the convergence of the CS algorithm and improving the quality of the reconstructed images. The proposed CS SAR method is applied to microwave and millimeter wave imaging systems for non‐destructive evaluation of materials embedded in stratified media. Three different specimens under test are measured by conventional uniform sampling and by random under‐sampling with 20% or 30% spatial points of the uniform sampling. The reconstructed images show that, albeit having much less measurement points, the proposed CS method achieves better image quality and lower background artefacts than the images reconstructed from the fully‐sampled uniform measurements.

Compressed sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. It holds valuable implications for wireless sensor networks because power and bandwidth are limited resources. In this paper, applying the theory of compressed sensing to the practical sensor network data recovery problem, we compare the performance of different CS reconstruction algorithms combined with wavelet and discrete cosine transform (DCT) basis. We demonstrate empirically that DCT is good for sinusoid oscillatory data while wavelet is good for data with point-like singularities. Furthermore, comparison on reconstruction algorithms shows basis pursuit (BP) is best in term of PSNR performance and computing time. In addition, benefit of CS for noisy channel of sensor network is tested and how to achieve good performance in noisy channel is discussed.

This paper aims to investigate the problem of low-dose computed tomography (CT) reconstruction with prior image constraints using the compressed sensing (CS) theorem. The CS theorem states that images can be reconstructed from under-sampled data in an adequate or transfer domain without introducing noticeable artifacts by solving a convex optimization problem if the source signals are sparse. To describe the sparsity, a model of piecewise constant source distribution has recently been assumed for image reconstruction by minimizing the total variance (TV) of the image density distribution in the Fourier domain. However, the assumption may not hold for complicated image structures. It has been observed that a prior image from the same subject or anatomy can provide excellent information to the image to be reconstructed. Based on this observation, this study investigates the problem of image reconstruction from under-sampled data by minimizing the difference between the prior image and the concerned image to be estimated with data constraints in the Fourier domain. Compared to the TV criterion, this presented method doesn't require the piecewise constant assumption where the similarity between the two images specifies a new priori model for a new cost function. The presented method was tested by computer simulations using the Shepp-Logan phantom. In noise-free case, only 64 projections around the phantom are needed to produce an accurate reconstruction. The reconstruction remained excellent until the number of projections was reduced to 22 when a high similarity exists between the prior and concerned images while the well-known filtered backprojection reconstruction failed. In cases with noise variance at 1% level, the signal-to-noise of the reconstruction by presented CS-based approach dropped rapidly when the number of projections decreased from 64 to 22. This investigation reveals the high sensitivity of the CS-based approach for low-dose CT image reconstruction. Modification of the cost function to consider data statistics is needed.

Event Abstract Back to Event A combined Compressed Sensing Super-Resolution Diffusion and gSlider-SMS acquisition/reconstruction for rapid sub-millimeter whole-brain diffusion imaging. Kawin Setsompop1, Lipeng Ning2 and Yogesh Rathi2* 1 Harvard Medical School, Massachusetts General Hospital, United States 2 Harvard Medical School, Brigham and Women’s Hospital, United States Purpose: Submillimeter isotropic diffusion imaging (DI) is made difficult by long acquisition time and low SNR. Slider-SMS acquisition (1) has recently been proposed to provide large improvement to SNR efficiency for DI, by allowing a large number of imaging slices to be acquire simultaneously through the combined use of SMS parallel imaging and super-resolution approaches. Further improvement to this acquisition with a new generalized Slider approach (gSlider) is also being proposed (2), which utilizes RF encoding to improve the orthogonality of the slice-encoding basis for super-resolution, to enable high quality 5 simultaneous slice super-resolution, which when combines with SMS parallel imaging can achieve highly efficient 10 simultaneous slices DI (gSlider x MB = 5x2). In this work, we provide further improvement to this acquisition by incorporating the framework of Compressed Sensing for Super-Resolution Diffusion (CS-RSD) proposed in (3) to gSlider-SMS. This enables acquisition acceleration through undersampling of the gSlider slice-encoded super-resolution acquisitions needed for super-resolution reconstruction of each diffusion direction (with different random undersampling for different diffusion directions). Such acquisition undersampling is made possible through sparsity enforce reconstruction where the diffusion signal in each voxel of the final high-resolution image is enforced to be sparse in the basis of spherical ridgelets. We demonstrate that the incorporation of the CS-RSD approach enables a further 3x? efficiency gain to an already highly efficient 10 simultaneous slice gSlider-SMS acquisition. This permits, for the first time, high quality 860um whole-brain DI at high b-value to be perform in a relevant clinical timeframe of 8 minutes. Method: gSlider-SMS data with 10 simultaneous slice acquisition (gSlider×MB = 5×2) were acquired in a healthy volunteer on the 3T CONNECTOM system using custom-built 64-channel array. Imaging parameters were: 860μm iso; FOV 220×163.4×130 mm3; p.f. 6/8; TE = 64ms and TR per thick-slice volume = 4.2s; effective echo spacing = 0.32ms, 64 directions at b=2000 s/mm2 with interspersed b0 every 10 volumes, where for each diffusion direction, imaging were performed 5 times for different RF gSlider encoding, total scan-time ~25 min. Background phase removal was performed using real value diffusion algorithm (6). Reconstruction for full sampled Slider encoding data were performed using Tikhonov regularized super-resolution reconstruction to represent fullysampled acquisition for comparison. For incorporation of CS-RSD, the 5 different gSlider slice-encode imaging per diffusion direction were randomly undersampled to provide three times acceleration to result in an effective acquisition time of ~8 min. This accelerated acquisition is reconstructed using algorithm proposed in (3) and compared with the fully sampled reconstruction. Results: Figure (1) shows the acquired thick-slice images and the reconstructed high-resolution diffusion-weighted images obtained using the Tikhonov regularization and the compressed-sensing approach, respectively. The high-resolution image obtained using the compressed-sensing approach has the lowest noise level due to the sparse representation using spherical ridgelets. Figure (2) shows the corresponding colored-coded diffusion tensor images for the three diffusion MRI volumes, respectively.

The paper proposes procedure for the watermarking of the magnetic resonance images (MRI) using Compressive Sensing approach. The watermark is created as a pseudo random sequence, which is embedded into the set of 2D discrete Fourier transform (2D DFT) coefficients of the observed image. The watermarking coefficients are selected along the radial lines in 2D DFT domain. In order to provide successful watermark detection, regardless the radial lineation, the watermark spreading is proposed. The experimental results prove that the proposed embedding procedure provides successful protection of MRI images even in the case when very small number of CS measurements is used for reconstruction. The efficiency of watermark detection is tested after the repeated Compressive Sensing procedure, as well as under the strong noise disturbances.

Abstract. Over the past decade hyper spectral (HS) image analysis has turned into one of the most powerful and growing technologies in the field of remote sensing. While HS images cover large area at fine spectral resolution, their spatial resolutions are often too coarse for the use in various applications. Hence improving their resolution has a high payoff. This paper presents a novel approach for super-resolution (SR) of HS images using compressive sensing (CS). Besides ill-posedness of SR problem, the main challenge in HS super-resolution is to preserve spectral contents among all bands while increasing their spatial resolutions. In this work, we first obtain an initial estimate of the super-resolution on a reduced dimension HS data. The HS observations of different wavelengths are represented as linear combination of smaller number of basis image planes (BIPs) using principal component analysis (PCA). The novelty of our approach lies in using CS based approach to super-resolve the most informative PCA transformed image representing highest spectral variance (i.e. the first principal component). Our approach uses low and high spatial resolution dictionaries of patches generated by random sampling of raw patches of PCA transformed images that are generated using the training images having similar statistical properties. Using the sparsity constraint, low resolution test patch is represented as a sparse linear combination of relevant dictionary elements adaptively, that leads to initial estimate of super-resolved PCA image having maximum spectral variability. Since SR is an ill-posed problem, we obtain the final solution using a regularization framework considering the sparse coefficients obtained by the CS approach and the autoregressive (AR) parameters obtained from the initial estimate. The remaining PCA images are up-scaled using regularization, considering the same AR parameters which were obtained from super-resolved PCA image having maximum spectral variability. Experiments are conducted on real HS images collected by Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). Visual inspections and quantitative comparison confirm that our method enhances spatial information without introducing significant spectral distortion.

The theory of compressed sensing (CS) leverages upon structure of signals in order to reduce the number of samples needed to reconstruct a signal, compared to the Nyquist rate. Although CS approaches have been proposed for ultrasound (US) imaging with promising results, practical implementations are hard to achieve due to the impossibility to mimic random sampling on a US probe and to the high memory requirements of the measurement model. In this paper, we propose a CS framework for US imaging based on an easily implementable acquisition scheme and on a delay-and-sum measurement model.

We know that COVID-19 has been considered a pandemic and various types of symptoms are analyzed by the doctors. Various cases belonging to COVID-19 are asymptomatic and due to this fact the disease is not analyzed at an initial stage and the condition of the patient will be critical. So, the purpose of this work is to provide a solution that will find out the highly precise test result of COVID-19. Magnetic Resonance Imaging, CT Scan & Lung Ultrasound are some of the methods which can provide the exact results for the testing. But the problem associated with these imaging modalities is that they are time-consuming and the data provided by these modalities are large enough to store or transmit. A compression technique is required which can reduce the time as well as data size. Computed Tomography with Compressive Sensing (CS) Technique is used as an approach to tackle the above-stated problem. To analyze the fact that this technique is efficient, we consider the Computed Tomography-based Chest images of COVID-19 infected patients and apply the CS technique (Basis Pursuit) with Discrete Cosine Transform as a representation basis and Gaussian as a measurement matrix. As a result of this study, we find out three parameters, PSNR, SSIM & FSIM, to visualize the efficiency of the reconstruction strategy. This work concludes that the Computed Tomography approach with the help of CS can be used for fast and efficient imaging for COVID-19 as well as other diseases of the same kind.

Digital projections are image intensity sums taken along directed rays that sample whole pixel values at periodic locations along the ray. For 2D square arrays with sides of prime length, the Discrete Radon Transform (DRT) is very efficient at reconstructing digital images from their digital projections. The periodic gaps in digital rays complicate the use of the DRT for efficient reconstruction of tomographic images from real projection data, where there are no gaps along the projection direction. A new approach to bridge this gap problem is to pool DRT digital projections obtained over a variety of prime sized arrays. The digital gaps are then partially filled by a staggered overlap of discrete sample positions to better approximate a continuous projection ray. This paper identifies primes that have similar and distinct DRT pixel sampling patterns for the rays in digital projections. The projections are effectively pooled by combining several images, each reconstructed at a fixed scale, but using projections that are interpolated over different prime sized arrays. The basis for the pooled image reconstruction approach is outlined and we demonstrate the principle of this mechanism works.