MTF behavior of compressed sensing MR spectroscopic imaging

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.

The Modulation Transfer Function (MTF) is a major parameter for high resolution optical remote sensing systems, indicating how spatial frequencies are transmitted and weakened by the imaging global chain. Assessing MTF is thus a very important task during both the in-flight commissioning period and the routine monitoring phases. Classical in flight MTF measurement methods are based upon devoted well known patterns such as knife edge patterns. These techniques induce heavy constraints upon satellite payload programming taking into account nebulosity conditions and pattern ground maintenance. Moreover, for high MTF systems, MTF assessment proves to be difficult because the point spread function has a too reduced extension. Another solution consists in taking two images of the same scene, one in a high resolution mode and the other one in a lower resolution mode. When the resolution ratio is high enough (typically higher then 3), it is possible to simulate the lower resolution image through convolution with a filter and undersampling. The least square method consists in an iterative process, according to which the convolution filter evolves in order to minimize a least square criterion measuring the difference between the simulation and the low resolution image. Once the process has converged, taking the Fourier Transform of the convolution filter gives an estimation of the ratio between low resolution image MTF versus high resolution image MTF. This method may be successfully applied to remote sensing systems such as Quickbird, Ikonos, SPOT5 and future PLEIADES-HR to assess MTF in the multispectral mode. The goal of this paper is to present the MTF assessment method, the way it was validated through simulations and its application within SPOT5 context.

In this work, the effect of noise on the precision in the modulation transfer function (MTF) calculation using different phantoms is investigated. Three different techniques are studied, based on three different phantoms: edge, bar, and star bar. For each technique, theoretical expressions for the standard deviation and the signal to noise ratio (SNR) of the MTF are derived. In addition, Monte Carlo simulations are carried out to study the accuracy and precision of all the three techniques. Using the analytic expressions for the MTF calculation, statistical fluctuations of noise in the phantom images are propagated to MTF values. Then, for each frequency the standard deviation and the SNR of the MTF are calculated. Monte Carlo simulations are carried out for each phantom image and for different noise level. Images are artificially generated following a procedure that simulates sampling, blurring, and noise present in a real phantom image and takes into account the attenuation of each phantom. Then, oversampling procedures are applied to these images to obtain presampled MTFs. In all three techniques the standard deviation of the MTF is proportional to that of the noise in the image. For the edge image, the standard deviation is proportional to the frequency f, whereas for the bar and star bar techniques it is proportional to the square root of f. Regarding the precision, theoretical expressions and simulations results agree that the bar technique shows the best precision for all the frequencies and all the noise levels analyzed in this study. In addition, simulation results show how, for large levels of noise, the edge technique gives rise to large bias errors at high and medium frequencies. Finally, the precision of the star bar technique is similar to that of the bar technique for isotropic systems, but worse for nonisotropic ones. The uncertainties in the MTF calculation with the edge technique are larger than with the bar technique, and the differences increase with the frequency. On the one hand, the stronger dependency on the frequency shown by the standard deviation of the MTF makes the precision gets worse faster in the edge technique. On the other hand, in the case of the edge and for high levels of noise, differentiation produces line spread functions (LSF) with a poor SNR, increasing erroneously the MTF and worsening accuracy.

Multi-aperture optical telescopes have been extensively studied owing to their high resolution, low cost, and light weight. The next generation of optical telescopes is predicted to be equipped with dozens or even hundreds of segmented lenses; therefore, it is necessary to optimize the arrangement of the lens array. This paper proposes a new structure called the Fermat spiral array (FSA) to replace the conventional hexagonal or ring array for the sub-aperture arrangement of a multi-aperture imaging system. The point spread function (PSF) and modulation transfer function (MTF) of the imaging system are compared in detail at single and multiple incident wavelengths. The FSA can effectively weaken the sidelobe intensity of the PSF, which is 12.8 dB lower on average than conventional ones with a single incident wavelength in the simulation and 4.45 dB lower in the experiment. A new MTF evaluation function is proposed to describe the mean level of MTF at mid-frequencies. The FSA can improve the MTF of the imaging system and weaken the ringing effect in the images. The imaging simulation indicates that FSA has superior imaging quality compared to conventional arrays, with a higher peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). The imaging experiments also achieve a higher SSIM with the FSA, which agrees well with the simulation results. The proposed FSA multi-aperture will help improve the imaging performance of next-generation optical telescopes.

Recently, there are a lot of study of direction of arrival (DoA) estimation using compressive sensing (CS). As CS is a new paradigm in signal processing, there are many aspects of this method that can be investigated. In the case of DoA estimation in noisy measurement, it is important to correctly determine a correct threshold of CS reconstruction, particularly when CS reconstruction is implemented using L 1 -norm minimization. Too small threshold value will make the correct DoA does not lies in CS reconstruction searching area, while too large threshold value will burden CS iteration to select a solution from a large number of possible solutions. In this paper, we derived an optimal threshold value for CS reconstruction for DoA estimation mathematically and verified the result using computer simulation. Using Gaussian noise model, we obtain the chi-square distribution of euclidean distance of noisy and noiseless received vector. We introduce the thresholding index κ to scale the standard deviation of chi-square distribution to determine the CS reconstruction threshold and simulate this value for various SNR. We find that the optimal κ value 0.5 to 1 for high noise environment, and optimal κ value 1 to 2 in low noise environment.

Compressive sensing (CS) has been proposed for images that are sparse under a certain transform domain. However, many natural images are not strictly sparse in the transform domain, causing a tail-folding effect that degrades the performance of the CS reconstruction. To decrease such effect, a sparse-filtering (SF) in Directional Lifting Wavelet Transform (DLWT) domain based Bayesian compressive sensing (BCS) algorithm (DLWT-SF-TSW-BCS) is proposed. At the encoder, DLWT, an efficient multi-scale geometrical analysis (MGA) tool, is used to produce the sparse representation for natural images. Then sparse-filtering is adopted to cut off the small DLWT coefficients before random measurement. At the decoder, the interscale tree-structure redundancy in DLWT domain is further exploited in Bayesian reconstruction. Experimental results show that the proposed DLWT-SF-TSW-BCS algorithm significantly outperforms other state-of-the-art CS reconstruction algorithms, for example, peak signal to noise ratio (PSNR) gain up to 10.00 dB over the tree structured wavelet compressive sensing (TSW-CS).

The presampling modulation transfer function (MTF) of a digital imaging system is commonly determined by measuring the system’s line spread function (LSF) using a narrow slit or differentiating the detector’s edge spread function (ESF) with an edge device. The slit method requires precise fabrication and alignment of a slit as well as a high radiation exposure. The edge method [3] is a complicated image processing procedure, requiring determination of the edge angle, reprojection, sub-binning, smoothing and differentiating the ESF, and spectral estimation. In this paper, a simple method is employed to evaluate the MTF using an edge device. The image processing procedures required by this method involve simply the determination of the over-sampling rate and the Fourier transform of the modified ESF. Differentiation and signal to noise ratio (SNR) improvement are jointly applied in the Fourier domain. The MTFs obtained by this simple method are compared to the theoretical MTF and the previously proposed more complicated edge method. The experimental results show that the proposed method provides a simple, accurate and convenient measurement of the presampling MTF for digital imaging systems.

In this paper, we address the problem of green Compressed Sensing (CS) reconstruction within Internet of Things (IoT) networks, both in terms of computing architecture and reconstruction algorithms. The approach is novel since, unlike most of the literature dealing with energy efficient gathering of the CS measurements, we focus on the energy efficiency of the signal reconstruction stage given the CS measurements. As a first novel contribution, we present an analysis of the energy consumption within the IoT network under two computing architectures. In the first one, reconstruction takes place within the IoT network and the reconstructed data are encoded and transmitted out of the IoT network; in the second one, all the CS measurements are forwarded to off-network devices for reconstruction and storage, i.e., reconstruction is off-loaded. Our analysis shows that the two architectures significantly differ in terms of consumed energy, and it outlines a theoretically motivated criterion to select a green CS reconstruction computing architecture. Specifically, we present a suitable decision function to determine which architecture outperforms the other in terms of energy efficiency. The presented decision function depends on a few IoT network features, such as the network size, the sink connectivity, and other systems’ parameters. As a second novel contribution, we show how to overcome classical performance comparison of different CS reconstruction algorithms usually carried out w.r.t. the achieved accuracy. Specifically, we consider the consumed energy and analyze the energy vs. accuracy trade-off. The herein presented approach, jointly considering signal processing and IoT network issues, is a relevant contribution for designing green compressive sampling architectures in IoT networks.

Image spatial resolution reflects the ability of an optical system to capture detailed information about an object. Compared to Low-resolution (LR) images, High-resolution (HR) images contain greater pixel density and textural detail. In the experiments, it is difficult to obtain ideal HR images due to the effects of acquisition equipment and image degradation. To address the problems, this paper proposes a HR optical image reconstruction method based on adaptive sparse dictionary. The experimental show that the area of the modulation transfer function (MTF) curve of the reconstructed image is improved by 16.41%, which represents the increase in the frequency components it contains. Meanwhile the cut-off resolution is improved from 0.2692cy/pix to 0.4018cy/pix. The method in paper achieves good results in both reconstruction efficiency and accuracy. The peak signal-to-noise ratio (PSNR) of the reconstructed image is improved from 20.1650 to 28.0192. The feature similarity (FSIM) and detail retention are above 90%.

The image quality (IQ) of imaging systems must be sufficiently high for image‐guided radiation therapy (IGRT). Hence, users should implement a quality assurance program to maintain IQ. In our routine IQ tests of the kV cone‐beam CT system (Elekta XVI), image noise was quantified by noise standard deviation (NSD), which was the standard deviation of CT numbers measured in a small area in an image of an IQ test phantom (Catphan), and the high spatial resolution (HSR) was evaluated by the number of line‐pairs (LPN) visually recognizable in the image. We also measured the image uniformity, the low contrast resolution, and the distances of two points for geometrical accuracy. For this study, we did an additional evaluation of the XVI data for 12 monthly IQ tests by using noise power spectrum (NPS) for noise, modulation transfer function (MTF) for HSR, and CT number‐to‐density relationship. NPS was obtained by applying Fourier analysis in a small area on the uniformity test section of Catphan. The MTF analysis was performed by applying the Droege‐Morin (D‐M) method to the line‐pair bar regions in the phantom. The CT number‐to‐density relationship was obtained for insert materials in the low‐contrast test section of the phantom. All the quantities showed a noticeable change over the one‐year period. Especially the noise level improved significantly after a repair of the imager. NPS was more sensitive to the IQ change than NSD. MTF could provide more quantitative and objective evaluation of HSR. The CT number was very different from the expected CT number, but the CT number‐to‐density curves were constant within 5% except for two months. Since the D‐M method is easy to implement, we recommend using MTF instead of LPN even for routine QA. The IQ of the imaging systems was constantly changing; hence, IQ tests should be periodically performed. Additionally, we found the importance of IQ tests after every service work, including detector calibration as well as preventive maintenance.PACS number(s): 87.56Da, 87.57.C‐, 87.57.N‐, 8757.Q‐

Deep-learning-based image reconstruction and noise reduction methods (DLIR) have been increasingly deployed in clinical CT. Accurate image quality assessment of these methods is challenging as the performance measured using physical phantoms may not represent the true performance of DLIR in patients since DLIR is trained mostly on patient images. In this work, we aim to develop a patient-data-based virtual imaging trial framework and, as a first application, use it to measure the spatial resolution properties of a DLIR method. The patient-data-based virtual imaging trial framework consists of five steps: (1) insertion of lesions into projection domain data using the acquisition geometry of the patient exam to simulate different lesion characteristics; (2) insertion of noise into projection domain data using a realistic photon statistical model of the CT system to simulate different dose levels; (3) creation of DLIR-processed images from projection or image data; (4) creation of ensembles of DLIR-processed patient images from a large number of noise and lesion realizations; and (5) evaluation of image quality using ensemble DLIR images. This framework was applied to measure the spatial resolution of a ResNet based deep convolutional neural network (DCNN) trained on patient images. Lesions in a cylindrical shape and different contrast levels (-500, -100, -50, -20, -10 HU) were inserted to the lower right lobe of the liver in a patient case. Multiple dose levels were simulated (50%, 25%, 12.5%). Each lesion and dose condition had 600 noise realizations. Multiple reconstruction and denoising methods were used on all the noise realizations, including the original filtered-backprojection (FBP), iterative reconstruction (IR), and the DCNN method with three different strength setting (DCNN-weak, DCNN-medium, and DCNN-strong). Mean lesion signal was calculated by performing ensemble averaging of all the noise realizations for each lesion and dose condition and then subtracting the lesion-present images from the lesion absent images. Modulation transfer functions (MTFs) both in-plane and along the z-axis were calculated based on the mean lesion signals. The standard deviations of MTFs at each condition were estimated with bootstrapping: randomly sampling (with replacement) all the DLIR/FBP/IR images from the ensemble data (600 samples) at each condition. The impact of varying lesion contrast, dose levels, and denoising strengths were evaluated. Statistical analysis with paired t-test was used to compare the z-axis and in-plane spatial resolution of five algorithms for five different contrasts and three dose levels. The in-plane and z-axis spatial resolution degradation of DCNN becomes more severe as the contrast or radiation dose decreased, or DCNN denoising strength increased. In comparison with FBP, a 59.5% and 4.1% reduction of in-plane and z-axis MTF (in terms of spatial frequencies at 50% MTF), respectively, was observed at low contrast (-10 HU) for DCNN with the highest denoising strength at 25% routine dose level. When the dose level reduces from 50% to 12.5% of routine dose, the in-plane and z-axis MTFs reduces from 92.1% to 76.3%, and from 98.9% to 95.5%, respectively, at contrast of -100 HU, using FBP as the reference. For most conditions of contrasts and dose levels, significant differences were found among the five algorithms, with the following relationship in both in-plane and cross-plane spatial resolution: FBP>DCNN-Weak>IR>DCNN-Medium>DCNN-Strong. The spatial resolution difference among algorithms decreases at higher contrast or dose levels. A patient-data-based virtual imaging trial framework was developed and applied to measuring the spatial resolution properties of a DCNN noise reduction method at different contrast and dose levels using real patient data. As with other non-linear image reconstruction and post-processing techniques, the evaluated DCNN method degraded the in-plane and z-axis spatial resolution at lower contrast levels, lower radiation dose, and higher denoising strength.

Compressed sensing (CS) algorithms exploit sparseness properties to reconstruct high spatial resolution magnetic resonance (MR) images from k-space data acquisitions significantly under sampled to reduce imaging times. CS algorithm effectiveness is frequently shown using under-sampled k-space data from NxN simulated images. These demonstration reconstructions are near perfect with quality higher than reconstructions using under-sampled NxN experimental k-space data sets. These differences are explained in terms of the interaction between the explicit transform domain sparsity requirement employed during iterative CS reconstruction and an inherent frequency domain property of the discrete Fourier transform (DFT). We report on experiments to overcome the limitations imposed by this DFT property by modifying the CS objective function to use a sparseness transform with a resolution higher that the standard transform related to the acquired NxN data matrix size. We demonstrate the relative effectiveness and limitations of standard CS and our proposed highresolution k-space extrapolation enabled (Hi-KEE) CS reconstruction on underand fully-sampled, simulated and experimental MR k-space data. (8 pages)

Satellite imagery always has low-resolution causing poor application in practice because the serious degradation in imaging is resulted in many factors such as atmospheric turbulence, cloud, and aberration of optical system. To reconstruct the degraded remote sensing images with a high quality, we designed an algorithm to estimate the system modulation transfer function (MTF) accurately. Phase congruency is employed to detect the edges and corners of the image first, then the significant edges, which are utilized to estimate the edge spread function (ESF) using inclined edge method, are picked up from above features through a certain line detection measurement. An image restoration algorithm based on total variation (TV) is introduced to deconvolute the degraded image with the estimated MTF which is derived from the ESF. The experiments show that this method is adaptive and efficient to recover the remote sensing images taken from a Chinese Satellite. The restored images with a higher resolution and higher signal-to-noise ratio (SNR) will improve the applications greatly.

Using a gradient optimization method with objective functions formulated in terms of a signal-to-noise ratio (SNR) calculated at given values of the prescribed spatial ground resolution, optimization problems of geometrical parameters of a distributed optical system and a charge-coupled device of a space-based optical-electronic system are solved for samples of the optical systems consisting of two and three annular subapertures. The modulation transfer function (MTF) of the distributed aperture is expressed in terms of an average MTF taking residual image alignment (IA) and optical path difference (OPD) errors into account. The results show optimal solutions of the optimization problems depending on diverse variable parameters. The information on the magnitudes of the SNR can be used to determine the number of the subapertures and their sizes, while the information on the SNR decrease depending on the IA and OPD errors can be useful in design of a beam combination control system to produce the necessary requirements to its accuracy on the basis of the permissible deterioration in the image quality.

Compressed sensing (CS) enables accurate CT image reconstruction from low-dose measurements, due to the sparsifiable feature of most CT images using total variation (TV). The CS reconstruction is formulated as either a constrained problem to minimize the TV objective within a small data fidelity error, or an unconstrained problem to minimize the data fidelity error with TV regularization. However, the conventional solutions to the above two formulations are either computationally inefficient or involved with inconsistent regularization parameter tuning. In this work, we propose an optimization algorithm for cone-beam CT (CBCT) CS reconstruction which overcomes the above two drawbacks. The data tolerance is well estimated using the measured data, as most of the projection errors are from Poisson noise. We adopt the TV optimization framework with data fidelity as constraints. To accelerate the convergence, we first convert such a constrained optimization using a barrier method into a similar form to the conventional TV-regularization reconstruction but with an automatically adjusted penalty weight. The problem is then solved efficiently by gradient projection. The proposed algorithm is referred to as Accelerated Barrier Optimization for CS (ABOCS). As demonstrated on Shepp-Logan and head phantoms, ABOCS achieves consistent performances using the same parameters on scans with different datasets, while the TV-regularization method needs a large-scale tuning on the penalty weight. ABOCS also requires less computation time than ASDPOCS in Matlab by more than 10 times. ABOCS is further accelerated on GPU to reconstruct a 3D Shepp-Logan volume of 256×256×256 voxels in less than 20 mins using 10% projections, and the image quality is comparable to that of the full-view FDK reconstruction. We propose ABOCS for CBCT reconstruction. As compared to other published CS-based algorithms, our method has attractive features of fast convergence and consistent parameter setting for different datasets.