Resolution evaluation of MR images reconstructed by iterative thresholding algorithms for compressed sensing

The iterative soft thresholding algorithm (ISTA) is one of the most popular optimization algorithms for solving the regularized least squares problem, and its linear convergence has been investigated under the assumption of finite basis injectivity property or strict sparsity pattern. In this paper, we consider the regularized least squares problem in finite- or infinite-dimensional Hilbert space, introduce a weaker notion of orthogonal sparsity pattern (OSP) and establish the Q-linear convergence of ISTA under the assumption of OSP. Examples are provided to illustrate the cases where the linear convergence of ISTA can be established only by our result, but cannot be ensured by any existing result in the literature.

The low-rank plus sparse (L+S) decomposition model enables the reconstruction of undersampled dynamic magnetic resonance imaging (MRI) data. Solving for the L and S components is anonsmooth composite convex minimization problem. While current techniques for this model are based on the classical iterative soft thresholding algorithm (ISTA), accelerated methods can be applied to obtain faster rate of convergence of the algorithm. This paper proposes two alternative methods for solving the L+S problem, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other based on the recent proximal optimized gradient method (POGM). Numerical results suggest faster convergence than the traditional ISTA, while preserving its computational simplicity.

The low-rank plus sparse (L+S) decomposition model enables the reconstruction of under-sampled dynamic parallel magnetic resonance imaging (MRI) data. Solving for the low-rank and the sparse components involves non-smooth composite convex optimization, and algorithms for this problem can be categorized into proximal gradient methods and variable splitting methods. This paper investigates new efficient algorithms for both schemes. While current proximal gradient techniques for the L+S model involve the classical iterative soft thresholding algorithm (ISTA), this paper considers two accelerated alternatives, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other with the recent proximal optimized gradient method (POGM). In the augmented Lagrangian (AL) framework, we propose an efficient variable splitting scheme based on the form of the data acquisition operator, leading to simpler computation than the conjugate gradient (CG) approach required by existing AL methods. Numerical results suggest faster convergence of the efficient implementations for both frameworks, with POGM providing the fastest convergence overall and the practical benefit of being free of algorithm tuning parameters.

Occupational exposure to static magnetic fields (SMF) is a concern in relation to magnetic resonance imaging (MRI) system operators. Bodily movements inside the stray field around an MRI system induce an electric current inside the body, and this magnetically induced current can cause temporary sensational changes. Although self-motivated motion control near MRI equipment is recommended in order to prevent these effects, a feasible and safe working procedure is required from a health and safety management viewpoint. In this paper, a procedure involving a restricted access area set at a distance of 30 cm from the end of a 3 T MRI system is compared with a protocol in which self-motivated motion control was used (as recommended by the International Commission on Non-Ionizing Protection guidelines). The effects of this safe working procedure on occupational SMF exposure levels and worker performance were evaluated using Hall sensors and a motion capture system. Subjects performed the protocol for head MRI examination both with and without the proposed safe working procedure. The values for maximum field exposure (peak B) were reduced for all subjects using the safe working procedure. The average peak B also decreased by approximately 26%, compared with the results obtained without any restrictions (conventional protocol) ( $p , $t$ -test). Motion analysis of the subjects indicated that the minimum approach distance to the MRI equipment increased due to the adoption of the restricted access area ( $p , $t$ -test), while slight changes were also observed in sojourn time and the differences of the position along the $z$ -axis ( $\Delta z$ , $p , $t$ -test). However, there were no significant differences in the parameters more closely related to worker performance (e.g., distance moved and velocity) when using the protocols with or without the safe working procedure. These results suggest that this simple safe working procedure may be applied to MRI system operation in order to reduce occupational SMF exposure, without noticeable changes in worker performance.

The most important advantage of 3.0-T magnetic resonance (MR) imaging systems is their increased signal-to-noise ratio (SNR) compared with 1.5-T systems. The higher SNR can be used to shorten acquisition time, achieve higher spatial resolution, or a combination of the two, thereby improving image quality and clinical diagnosis. In fact, 3.0-T MR imaging systems have already proved superior to 1.5-T systems in neuroradiologic and musculoskeletal applications. In the abdomen, 3.0-T MR imaging is uniquely beneficial for techniques such as enhanced and nonenhanced hepatic imaging, diffusion-weighted imaging, angiography, MR pancreatography, and colonography. Admittedly, 3.0-T abdominal imaging has important technical limitations, such as standing wave artifact, chemical shift artifact, susceptibility artifact, and safety issues such as increased energy deposition within the patient's body. Furthermore, 3.0-T abdominal MR imaging is still in the early stages of development and requires substantial modifications of the pulse sequences and hardware components used for 1.5-T imaging. Nevertheless, the ability to obtain physiologic and functional information within reasonably short acquisition times with 3.0-T abdominal MR imaging bodies well for the future of this imaging technique.

Synthetic aperture radar (SAR) is widely used for ground observations owing to its all-weather and all-time capabilities. Sparse SAR reconstruction imaging, which can enhance SAR imaging performance, has emerged as a significant research area. The traditional sparse SAR reconstruction imaging method was successfully applied to raw SAR data processing. However, the computational complexity makes sparse reconstruction imaging difficult for large scenes. Meanwhile, because raw data are usually kept confidential, only limited data are available. To address the issue of how to use publicly available complex image data for sparse reconstruction and effectively improve image quality, this study proposes a joint L1- and F-norm edge-preservation-based sparse SAR reconstruction algorithm for complex images. The algorithm uses the gradient descent (GD) technique to optimize the L1-norm regularization and reconstruct the overall image information; the iterative soft thresholding algorithm (ISTA) to optimize the F-norm regularization and reconstruct the high-frequency image information; and fuses the two sets of reconstructed information to obtain SAR reconstructed images with characteristics such as edge preservation, clear texture, and high quality. The results show that, compared with traditional matched filtering (MF) imaging results, the joint L1- and F-norm results obtained for complex images have lower sidelobes, higher signal-to-noise ratio, and better target resolution ability; compared with the F-norm-based sparse SAR reconstruction imaging results, the joint L1- and F-norm method provides images with better edge texture clarity.

In this paper we continue to study the problem of efficient video coding based on compressive sensing. In our previous work we proposed CS-JPEG video codec, where dragon noiselet transform is applied to a differential frame computed as a residual between an input frame and its downsampled and upsampled version. The downsampled version of the frame is compressed via JPEG baseline, while the noiselet coefficients are subsampled, quantized, entropy encoded and embedded into the application header of the JPEG file. At the decoder side, an iterative soft thresholding algorithm (ISTA) with video block-matching and 3D filtering (VBM3D) used as the thresholding operator is applied. In this paper, we first introduce a fast ISTA based on simple temporal and spatial transforms with parameters which are randomly selected at each iteration, and show that the proposed approach reduces the recovery time by around 300 times. Second, we consider the codec parameters selection providing the best reconstruction quality for a given bit rate. Finally, we evaluate the codec performance on HD video sequences recorded by real-life street surveillance systems without camera motion and show that CS-JPEG with the fast decoding and the selected parameters provides 54.3% and 22.4% bit rate savings, in average, comparing with the fast implementations of H.264/AVC Intra or H.265/HEVC Intra, respectively.

Various deconvolution algorithms for acoustic source are developed to improve spatial resolution and suppress sidelobe of the conventional beamforming. To improve the computational efficiency and solution convergence of deconvolution, this paper proposes a Fourier-based improved fast iterative shrinkage thresholding algorithm. Simulations and experiments show that Fourier-based improved fast iterative shrinkage thresholding algorithm can achieve excellent acoustic identification performance, with high computational efficiency and good convergence. For Fourier-based improved fast iterative shrinkage thresholding algorithm, the larger the weight coefficient, the narrower the mainlobe width, and the better the convergence, but the spurious source also increases. The recommended weight coefficient for the array described herein is 3. In addition, like other Fourier-based deconvolution algorithms, Fourier-based improved fast iterative shrinkage thresholding algorithm using irregular focus grid can obtain better acoustic source identification performance than using the conventional regular focus grid.

Compromises in the design of a positron emission tomography (PET) insert for a magnetic resonance imaging (MRI) system should minimize the deterioration of image quality in both modalities, particularly when simultaneous demanding acquisitions are performed. In this work, the advantages of using individually read-out crystals with high-gain silicon photomultipliers (SiPMs) were studied with a small animal PET insert for a 7 T MRI system, in which the SiPM charge was transferred to outside the MRI scanner using coaxial cables. The interferences between the two systems were studied with three radio-frequency (RF) coil configurations. The effects of PET on the static magnetic field, flip angle distribution, RF noise, and image quality of various MRI sequences (gradient echo, spin echo, and echo planar imaging (EPI) at 1H frequency, and chemical shift imaging at 13C frequency) were investigated. The effects of fast-switching gradient fields and RF pulses on PET count rate were studied, while the PET insert and the readout electronics were not shielded. Operating the insert inside a 1H volume coil, used for RF transmission and reception, limited the MRI to T1-weighted imaging, due to coil detuning and RF attenuation, and resulted in significant PET count loss. Using a surface receive coil allowed all tested MR sequences to be used with the insert, with 45–59% signal-to-noise ratio (SNR) degradation, compared to without PET. With a 1H/13C volume coil inside the insert and shielded by a copper tube, the SNR degradation was limited to 23–30% with all tested sequences. The insert did not introduce any discernible distortions into images of two tested EPI sequences. Use of truncated sinc shaped RF excitation pulses and gradient field switching had negligible effects on PET count rate. However, PET count rate was substantially affected by high-power RF block pulses and temperature variations due to high gradient duty cycles.

PurposeEddy currents are inevitable in magnetic resonance imaging (MRI) systems. These currents are mainly induced by gradient fields. This study aims to propose a fast analytical method to calculate eddy currents induced by frequently switching gradient fields in a traditional C-shape MRI system.Design/methodology/approachFourier decomposition and magnetic vector potentials were used to calculate the eddy currents. Calculations with the proposed analytical method revealed the spatial distribution and temporal evolution of eddy currents.FindingsCalculation and Maxwell simulation results were consistent. The agreement between calculation and simulation results indicates that increasingly sophisticated structures could be developed. The calculated results could guide the design of improved gradient coils.Originality/valueEddy currents induced by gradient current are decomposed into currents induced by each time-harmonic component, and then adding them together to obtain complete contribution of the eddy current. The analytical method was used to characterize the properties of symmetric and asymmetric eddy currents induced by gradient coils in MRI systems. The analytical method can be used to improve the gradient shield during the design of the gradient coil in the MRI system.

This work presents an algorithm for the local subpixel estimation of the Point Spread Function (PSF) that models the intrinsic camera blur. For this purpose, the Bernoulli(0.5) random noise calibration pattern introduced in a previous article is used. This leads to a well-posed near-optimal accurate estimation. First the pattern position and its illumination conditions are accurately estimated. This allows for accurate geometric registration and radiometric correction. Once these procedures are performed, the local PSF can be directly computed by inverting a linear system. This system is well-posed and consequently its inversion does not require any regularization or prior model. The PSF estimates reach stringent accuracy levels with a relative error in the order of 2 to 5%.

Intracardiac echocardiography (ICE) is routinely used in many interventional procedures in cardiology. In these procedures ICE catheter is positioned with fluoroscopy guidance, which can be harmful due to ionizing X-ray radiation exposure. Positioning the ICE catheter using an interventional magnetic resonance imaging (MRI) system would enable procedures that are free of ionizing radiation, and complement MRI with its speed and image resolution. This paper presents a feasibility study of potential combination of these modalities demonstrating the visibility of a CMUT-based ICE catheter tip for positional guidance, minimum distortion of the MRI image, and the functionality of catheter components under high static and RF magnetic fields in MRI room.

Retinal images are often degraded with a blur that varies across the field view. Because traditional deblurring algorithms assume the blur to be space-invariant they typically fail in the presence of space-variant blur. In this work we consider the blur to be both unknown and space-variant. To carry out the restoration, we assume that in small regions the space-variant blur can be approximated by a space-invariant point-spread function (PSF). However, instead of deblurring the image on a per-patch basis, we extend individual PSFs by linear interpolation and perform a global restoration. Because the blind estimation of local PSFs may fail we propose a strategy for the identification of valid local PSFs and perform interpolation to obtain the space-variant PSF. The method was tested on artificial and real degraded retinal images. Results show significant improvement in the visibility of subtle details like small blood vessels.

Magnetic resonance (MR) imaging systems are uniquely able to acquire data simultaneously for the reconstruction of images from multiple sections, that is, for volumes up to 20 cm or more in length and for axial, coronal, and sagittal planes. A phantom has been developed that allows one to determine if the sections are of the desired thickness throughout the volume, if the sections are contiguous or the section spacing is as specified, if the central section is at the appropriate location, if the profile of the section is as specified by the manufacturer, if the signal strength is uniform for all sections, that the signal strength decreases in a consistent manner for second and subsequent echo images, and that gross spatial distortions are not present. Such measurements are essential for acceptance testing and quality control purposes over reasonably long volumes. The details of this new phantom are described, and results of its use with both low-and high-field-strength MR imaging systems are presented.

Currently in Magnetic Resonance Imaging (MRI) systems, most hardware failures are only detected after a component has stopped functioning properly. In many cases, this results in a downtime of the system. Moreover, sometimes defective parts are not identified correctly, which may result in more parts than necessary being replaced, causing extra costs. Often in MRI systems, hardware related problems have an impact on image quality. Given an imaging protocol and a well-functioning MRI system, certain image quality metrics have a normal range in a given patient population. Thus, such metrics will present a measurable behavior change in case of a hardware problem. We identified such simple and powerful metrics for signal-to-noise ratio, noise variance and symmetry in images for hardware failures related to Shimming and Local RF coils in this work. To be able to calculate these metrics with every MRI image during the clinical workflow, another constraint is the computation time. With the performance of quality metrics on machine learning algorithms and computation time, we are able to identify the failing MRI components with an accuracy of up to 0.96 AUROC.