Compressed sensing MRI: a review of the clinical literature
MRI is one of the most dynamic and safe imaging techniques available in the clinic today. However, MRI acquisitions tend to be slow, limiting patient throughput and limiting potential indications for use while driving up costs. Compressed sensing (CS) is a method for accelerating MRI acquisition by acquiring less data through undersampling of k-space. This has the potential to mitigate the time-intensiveness of MRI. The limited body of research evaluating the effects of CS on MR images has been mostly positive with regards to its potential as a clinical tool. Studies have successfully accelerated MRI with this technology, with varying degrees of success. However, more must be performed before its diagnostic efficacy and benefits are clear. Studies involving a greater number radiologists and images must be completed, rating CS based on its diagnostic efficacy. Also, standardized methods for determining optimal imaging parameters must be developed.
MRI is one of the pre-eminent imaging modalities used in clinical practice today. Its ability to provide soft-tissue contrast is unmatched by most, if not all other imaging modalities. MRI can survey and quantify metabolic and physiological features of tissue, yielding valuable information about pathological processes that would otherwise be difficult to assess non-invasively. Not to be overlooked, MRI does not expose patients to dangerous ionizing radiation, making it safer than CT, the modality most likely to replace MRI, when MRI is not available or contraindicated. These properties of MRI contribute to its potential to be the most versatile imaging tool available to physicians.
However, a major obstacle to realizing this potential in many applications is limited imaging speed. MR images are thus susceptible to motion-related artefacts, which may even necessitate sedation or anaesthesia. Relatively low temporal resolution limits MRI of body parts that move with respiration, such as in abdominal1 and cardiac imaging.2 Long scan times increase costs and limit the number of patients for whom MRI is available.3 For these reasons, physicians often seek alternate paths to diagnose patients and are routinely compelled to use CT instead of MRI, despite the added risk of exposure to ionizing radiation.4
The issue of long acquisition times in MRI stemming from segmented sampling of the k-space was recognized soon after its consideration as a clinical tool; attempts to accelerate MRI date to the late 1970s, before MRI was generally available for clinical use.3 Motivations for increasing imaging speed included the limitations described above and especially the demands of physiological measurements that require higher spatial and/or spectral resolutions.5 Because for a given sequence structure, the number of segments in k-space is a direct determinant of image acquisition time, methods for accelerating MRI commonly involve reducing their number, i.e. undersampling k-space. These approaches capitalize on the inherent redundancy in MR images, where individual points in k-space do not arise from distinct spatial locations.6 Examples of this strategy include partial Fourier reconstruction7 and parallel imaging (PI).8,9 PI has made its way into the mainstream of clinical imaging. This approach exploits the fact that concurrently collected signals from coils with different spatial sensitivities carry distinct information about spatial localization complementing conventional spatial encoding and allowing skipping acquisition of k-space points.10 However, PI acceleration factors >2 are not reliably achievable in the clinic, without unacceptable image degradation.1
Within the past decade, another technique has been developed and has been applied to accelerate MRI acquisition. Compressed sensing (CS) is also founded on the premise of reconstructing an image from an incompletely filled k-space.6,11,12 Unlike PI, however, in CS, no complementary information is collected. The inspiration for CS came from attempts to solve a somewhat related imaging problem: storage and transmission of increasingly large imaging data sets. The solution to this problem was lossy image compression, a process that reduces file size by permanently discarding certain data elements. Using a variety of algorithms, medical images can be successfully compressed while preserving diagnostic efficacy, even at compression ratios from 9 : 1 to 25 : 1.13 Advances in image compression prompted Candes et al11 and Donoho12 to raise a series of questions which Lustig et al6 summarized in the context of MRI: “Since the images we intend to acquire will be compressible, with most transform coefficients negligible or unimportant, is it really necessary to acquire all that data in the first place? Can we not simply measure the compressed information directly from a small number of measurements, and still reconstruct the same image, which would arise from the fully sampled set? Furthermore, since MRI measures Fourier coefficients …, the question is whether it is possible to do the above by measuring only a subset of k-space.”
Affirmative answers to these questions form the basis of CS for accelerating MRI acquisition. Operationally, the reconstructed image must be consistent with the Fourier transform of the acquired k-space data and have few large-valued coefficients when sparsely transformed. Mathematically, this entails solving an optimization problem, i.e. finding the image that minimizes this form:6
Since 2007, the body of literature concerning CS and its application to a multitude of different clinical MR applications has increased at a near-exponential rate (Figure 1a). However, publications are largely focused on technical aspects of methodology and implementation; few studies1,2,14−29 have examined the quality and diagnostic efficacy of accelerated CS images (Figure 1b). This review evaluates the literature assessing performance of CS for clinical applications, where diagnostic efficacy is of the utmost importance. Momentum for clinical use of CS continues to build, pushing this burgeoning technology towards the cusp of widespread clinical availability. It is imperative that clinical implementation be guided by an evidence base supporting its clinical validity and diagnostic utility. This review will thus identify the current evidence base and delineate remaining gaps in knowledge, to be addressed by future research.
A structured literature search was conducted using the PubMed database to identify all pertinent articles published as of June 2014. The search terms used were as follows: “compressed sensing MRI” and “compressive sensing MRI”. These searches yielded a total of 281 articles, 269 of which were unique. The references cited within these articles were probed for any additional relevant articles that were missed in the original searches. Of this contingent of articles, 18 articles1,2,14−29 survived our exclusion criteria and were included in the review. Articles were excluded from the review if they met any of the following criteria: language other than English; study of CS and related technology in applications other than medical MRI; studies exclusively investigating CS as a method or technology rather than its implementation and efficacy in one or more specific clinical applications; animal studies; and reviews.
In order to facilitate a meaningful analysis of the different study designs used across the clinical CS research, we grouped methods based on their fundamental assessment of two overarching attributes: (1) image quality or (2) diagnostic efficacy. We define image quality as any assessment or scoring of an image based on its inherent characteristics and diagnostic efficacy as any assessment or measurement of an image's utility in making an accurate diagnosis, in comparison with an external standard. Each of these two characteristics can be assessed qualitatively or quantitatively, as shown in Figure 2. All of the assessment criteria used by each of the studies is available in the Supplementary Table A.
Clinical applications of compressed sensing
Decades of research studying the effects of compression on different types of medical images has provided evidence that the “tolerance” of an image to compression is dependent on the modality and the nature of the anatomical and pathological content of the image.30 Therefore, the degree of compression implemented in the clinical setting is dependent upon these same factors.31 It stands to reason that CS, a technology related to image compression, should similarly be evaluated across the breadth of MRI applications and anatomical regions. The 18 articles included in this review evaluated the effect of CS on a wide range of MR applications (Figure 3). These studies assessed image quality at different acceleration rates and reported to what extent remained acceptable in the face of acceleration (Table 1).
|Compressed sensing MR application||Highest acceleration rate achieving “acceptable” image||Highest acceleration rate attempted|
|DCE-MRI (breast)14,16||10×,14 2×16||10×,14 4×16|
|MRS (brain and prostate)17||5×||10×|
|Phosphorous MRS (muscle)20||2×||3×|
|Vascular flow quantification25||4–5×||4–5×|
|Chemical shift imaging22||4.94×||6.42×|
|Liver MRI21||Not specified||Not specified|
Although CS is a method for accelerating imaging by undersampling k-space at acquisition, it can also be “simulated” by undersampling a complete k-space, i.e. discarding part of the k-space data prior to the inverse Fourier transform, which creates the image. This latter approach is more convenient in the research setting because multiple permutations of undersampling can be tested, without additional scan time. Additionally, all undersampled images can be compared with the fully sampled conventional reference image from which they were derived. Many researchers refer to this “simulation” of CS as retrospective CS or retrospective CS reconstruction.15–17,20,23,26,27 Standard undersampling of k-space at acquisition is often referred to as prospective CS or prospective undersampling to distinguish the two methods. Both prospective and retrospective study designs for CS image acquisition were observed among the 18 articles reviewed (Figure 4). 15 studies used only one of the 2 designs: 9 studies performed only prospective CS1,2,18,21,22,24,25,28,29 and 6 studies performed only retrospective CS.14–17,19,23 Three studies used both prospective and retrospective CS.20,26,27 In all three of these cases, CS was retrospectively simulated prior to the performance of prospective CS acquisitions. The rationale for performing both retrospective and prospective CS in the same study were: (1) to validate the CS technique;20 (2) to confirm that prospective undersampling did not affect the image quality results;26 and (3) to select a reconstruction algorithm prior to implementing it in a prospective study.27 No advantage in the achievable acceleration was discernable between studies using prospective or retrospective CS.
A total of 1306 sets of images were generated from the 275 subjects across the 18 articles. We define a “set” of images as the images acquired from a patient using a given acquisition method, reconstruction algorithm and acceleration rate. All 18 articles explained their methodology for creating these image sets. Each study generated several image sets, which they then compared to evaluate the quality of the images or diagnostic efficacy at one or more acceleration rate. A full breakdown of the image sets described by each study is included as Supplementary Table A.
Study subjects and image evaluators
Sample size and makeup is an important consideration when evaluating new imaging techniques, as is the number and state of blinding of the image evaluators.32 A total of 275 subjects were imaged across the 18 studies (range, 3–34; mean = 15.28; median = 11.5; standard deviation = 10.23). 7 studies imaged healthy subjects,15,19–21,23,24,27 and 11 imaged patients referred for the type of imaging under consideration1,2,14,16–18,22,25,26,28,29 (Figure 5).
Images were either evaluated by human readers or scored based on quantitative criteria. In the studies reviewed, there were 19 total human readers, 17 of whom were radiologists. Of these 17 radiologists, 8 were explicitly characterized as “board certified”. The other 9 radiologists were described as “experienced” in evaluating the types of images in their given studies. This experience ranged from 1 to 20 years. The two non-radiologist human readers were an MR physicist and a senior research radiographer, each with 7 years of experience with muscle imaging, the area of focus in this study.22 In 10 studies human readers rated images.1,15,18,21–23,26–29 In eight studies, accurate measurement of a quantitative metric with CS MRI (e.g. contrast uptake or metabolite concentration) was assessed.2,14,16,17,19,20,24,25 The breakdown of the number of image evaluators included across studies and the degree to which they were blinded to patient or image information is presented in Figures 6 and 7, respectively.
A wide range of acceleration factors was tested across the 18 studies. Since CS accelerates image acquisition by undersampling k-space, it follows that the average density of k-space sampling is inversely proportional to acceleration. For example, an acquisition that randomly samples only 25% of k-space would be accelerated by a factor of 4 relative to the same acquisition where all points in k-space are sampled. Such undersampling is achieved by a four-fold reduction of number of acquired k-space lines in Cartesian sampling; number of projections or spirals in radial or spiral sampling and number of k-space points in chemical shift imaging. This is because each type of k-space sampling has one dimension along which sampling is “free”: a line, a spoke, a spiral and time respectively.
Fully sampled images were often used as the gold-standard reference, and were either acquired, or already existed in the case of the retrospective CS reconstructions. Acceleration factors up to 12.5× were tested, achieving varying degrees of success in producing images insignificantly different from standard imaging techniques or of acceptable diagnostic efficacy relative to the standard images (Figure 8). All but four studies acquired or used fully sampled images as controls.1,25,27,29 Reasons for not employing this standard included: studies (1) aimed to test the effects of CS + PI relative to PI alone,1,29 (2) relied upon conservation of blood flow as an internal physiologic control,25 or (3) partial Fourier reconstruction accelerated 1.6× served as a gold standard.27
All eight studies that tested acceleration factors up to 2× reported diagnostically acceptable images or images not significantly different from gold standard images at a given degree of undersampling.15–17,19,20,23,26,28 In only two of these studies was acceleration also successfully pushed beyond 2×.15,17 Of the 27 tests of acceleration factors >2, 18 tests were successful while 9 failed to produce acceptable images. The highest degree of acceleration that yielded acceptable images was 12.5×, for contrast-enhanced MR angiography.27 Results of all acceleration factors tested in each study is included as Supplementary Table A.
Combined compressed sensing and parallel imaging
Eight studies combined CS with PI in order to multiply their maximum acceleration.1,2,18,21,22,25,28,29 All of these studies found that the combined methodology produced images deemed acceptable or not significantly different from fully sampled images, while employing acceleration rates from 2× to 7.2×, depending on the application. Five of these studies compared the combined method with the standard imaging protocol for the respective study's imaging application.2,18,21,22,28 One study used conservation of blood flow to the upper, lower and whole body as an internal control.25 The other two studies compared the images acquired by PI alone with those acquired with the combined CS + PI method.1,29 In all eight of these studies, the authors concluded that combining CS and PI results in better images than when PI is implemented on its own. The combination of CS and PI did not systematically increase the acceleration rates, yielding acceptable images in comparison with CS implemented on its own. Across all attempts to exceed an acceleration factor of 2×, six approaches (across five studies) were successful with combined CS + PI.1,18,22,25,29
Sparsifying transform and reconstruction
In addition to the data that are collected, CS image reconstruction depends on three additional factors, expressed in Equation (1): (a) the k-space undersampling strategy, (b) the sparsifying transform and (c) the value of the regularization parameter. The different parameter choices made by the authors of the reviewed studies are summarized in Table 2. Nine of the studies15–20,22,23,27 either reported the parameters explicitly or cited correspondingly in Greengard et al,33 Lustig and Pauly,34 Feng et al,35 Uecker et al,36 Zhang et al37 where each could be found, though the available information may have been incomplete. Simply describing the sparsifying transform as a wavelet type, for example, still leaves many details unclear as there are many types of wavelets, each with different properties.38 All of the studies utilized undersampling strategies, which either fully sampled the centre of k-space or sampled it more densely than the periphery of k-space. When Poisson disc or Gaussian sampling was used, the parameters of these distributions (minimum distance between points and its dependence on location in k-space for Poisson-disc sampling or width of the Gaussian sampling) were not always specified. While intuitive or semianalytic substantiation of the choice of sparsifying transform and sampling strategy can be found, the greatest challenge is presented by the regularization parameter. As seen in Table 2, the regularization parameter appears to depend on image type, acceleration factor, sparsifying transform, sampling scheme etc. Importantly, it also depends on how the data are scaled. Indeed, Equation (1) verifies that scaling the measured data S and the reconstructed image x by a factor of 2 also requires corresponding scaling of the regularization parameter. Thus, for the value of the regularization parameter to convey useful information, the scaling of the data needs to be described. Only one study, by Akcakaya et al,15 reported how the data were scaled. All studies noted that the value of the regularization parameter impacts perceived image quality, artefacts or synthetic appearance.
|Study||Sparsifying transform||Undersampling strategy||Regularization|
|Vasanawala et al1||Wavelet||Poisson disc|
|Wang et al14||Spatial finite difference or discrete wavelet transformation||Undersampling in both ky and kz phase-encoding directions using a 2D Gaussian random distribution|
|Akcakaya et al15||Sparsity in terms of the number of non-zero intensity voxels||The central k-space region is densely sampled in diamond-like shape with 24-point diagonal. The edges of the k-space were sampled using a zero-mean Gaussian-probability density||The regularization parameter was set to 2/500 of the maximum of the zero-filled image for the first 50 iterations and 2/100 of the maximum for the last 10 iterations|
|Smith et al16||Magnitude of image intensity gradient||The central k-space region is fully sampled. At higher frequencies the sampling density of phase encodes follows k−1, where k is spatial frequency||λ = 0.1|
|Geethanath et al17||Daubechies wavelet transform and total variation||The central k-space region is fully sampled in 2D. The extent of the fully sampled centre was dependent on the inverse of the acceleration factor. At higher k, the sampling density of phase encodes follows k−n, n is not specified||Experimentally determined λw = 0.001 and λTV = 0.005|
|Hsiao et al2||Poisson disc|
|Hsiao et al18||Wavelet transform||Variable density Poisson-disc k-space undersampling in phase encode (2D slices)||λ = 0.015|
|Madelin et al19||Discrete cosine transform and total variation||The 3D radial acquisition with the spherical co-ordinates of the spokes chosen following the Rakhmanov–Saff–Zhou algorithm||λw = 0.0005, 0.0010, 0.0025, 0.0050, 0.0075, 0.0100 and λTV = 0, 0.0005, 0.0010, 0.0025, 0.0050, 0.0075, 0.0100|
|Parasoglou et al20||PCA—principal components in time domain||The sampling density of phase encodes follows k−3 in ky–kz phase encodes||λpca = 0.01|
|Chandarana et al21||Total variation in space and time||Golden-angle scheme of 2D radial acquisition|
|Hollingsworth et al22||Daubechies 4 wavelet||Variable density Poisson-disc undersampling in ky–kz, with 24 × 24 fully sampled centre with quadratic fall in density from the k-space centre||λ = 0.1 determined by best match between CS reconstruction and reconstruction of the fully sampled data using RMSE and the SSIM|
|Sharma et al23||Daubechies 4 wavelet||Fully sampled centre of 10% i.e. 25 lines. Two sampling densities were evaluated k−2 and k−6 with the latter giving better performance||λ = 0.002 for 2×, 3×, 4× accelerations of T2-SE and 2× acceleration of T2-FLAIR; λ = 0.001 for T2-FLAIR at 3× and 4× accelerations|
|Tao et al24||Fourier||Full sampling of the central 20 rows of k-t space and the remaining k-t space being sampled with a uniform density, randomised pattern|
|Tariq et al25||k-space data were acquired with variable density Poisson-disc undersampling in two-phase-encoding directions|
|Worters et al26||Daubechies 4, in y–z||Gaussian-weighted variable density random sampling pattern|
|Rapacchi et al27||Total variation||Three schemes: a uniform distribution, a Gaussian-probability density distribution and a Poisson-disc distribution where disc radius increases with distance to the centre of k-space. For all sampling patterns, 10% of the samples were distributed in the centre of k-space to acquire fully low frequency points||Determined by best match between CS reconstruction and reconstruction of the fully sampled data using RMSE excluding voxels in the lower 10% of the intensity scale to a void background noise|
|Rosenkrantz et al28||Total variation in space and time||Golden-angle ordering of radial acquisitions|
|Zhang et al29||Wavelet||Variable density Poisson-disc k-space sampling|
Another relevant aspect of image reconstruction is its speed. Given non-linear and iterative nature of the available algorithms, the reconstruction is inherently slow. Tabulating their performance requires standardization of the task: type of acquisition, k-space undersampling strategy, sparsifying transform etc. and therefore is more appropriate for a technical review of CS. Nevertheless, long delay between image acquisition and its availability for review by a radiologist presents a barrier for the widespread clinical use of CS. Depending on the task and algorithm, the delay may be between 30 and 210 min.1,14,19 However, we remain optimistic that through a combination of increased central processing unit speeds, parallel computing, graphics processing unit implementation and maturation of algorithms, this impediment will be resolved over time.
The 18 articles varied substantially in their methods for evaluating images. Figure 9 presents the breakdown of the number of studies whose assessment methods fit each of the above classifications. 8 of the 16 quantitative assessments of image quality used radiologists as readers.15,21–23,26–29 Each reader rated images on a numerical scale, based on the delineation or clarity of a given set of anatomical landmarks or lesion borders, in addition to other criteria. The other eight articles that quantitatively evaluated image quality rated a CS image by comparing it to a measurement made with standard imaging. These comparisons included correlation between contrast uptake curves;14 voxel intensities;16 metabolite maps and intensities;17 ventricular volume, ejection fraction and various vascular flow rates;2 signal-to-noise ratio (SNR) and tissue sodium concentration;19 muscle phosphocreatine resynthesis rate;20 and various vascular velocity and flow rates.24,25 In the only article that qualitatively assessed image quality, Vasanawala et al1 asked radiologists to rate images as “good quality”, “limited” or “non-diagnostic”, to indicate their preference for images acquired via combined CS and PI or PI alone and to compare anatomical structure delineation between the two accelerated imaging methods.
Only three articles specifically assessed the diagnostic efficacy of CS MRI. In these studies, CS imaging was used to attempt diagnosis of brain lesions,23 abdominal lesions29 and either cardiac valvular insufficiency or extracardiac shunts.18 The qualitative assessments of diagnostic efficacy either asked radiologists to judge the clinical diagnostic quality of the reconstructed images23 or to select an image quality score threshold for diagnostic utility.29 Hsiao et al18 authored the only quantitative assessment of the diagnostic efficacy of CS MRI. In this study of cardiac imaging, two radiologists blinded to patient history were asked to note the presence of valvular regurgitation at any valve and to tabulate the presence of any intracardiac or extracardiac shunts. Their ability to accurately diagnose these pathologies using CS MRI, standard MRI and echocardiogram was compared. Echocardiogram was considered the gold standard for detecting these lesions. Intermodality agreement between CS MRI and echocardiogram was calculated for each of the two radiologists (AH and SSV). Sensitivity and specificity of CS MRI were also calculated with respect to echocardiography as the gold standard. Based on these measures, the authors concluded that the radiologists were able to reliably diagnose valvular insufficiency and extracardiac shunts with CS MRI.
Compressed sensing artefacts
Image artefacts affect perception and disrupt readers to varying degrees.39 Sharma et al23 (brain MRI), Worters et al26 (spine MSI) and Zhang et al29 (paediatric abdominal MRI) were the only studies we reviewed that systematically described artefacts observed in CS. In the study of brain MRI, artefacts became prominent and disruptive to diagnosis at acceleration factors >2×. The two primary artefacts observed in this study were “global ringing” and blurring of fine detail. The authors concluded that these artefacts would hinder the accurate diagnosis of pathology but suggested that 2×-accelerated data acquisition might be possible for sequences with higher native spatial resolution. Worters et al26 described “slight blurring” of CS reconstructed images, which they suggested was due to the denoising effect of CS reconstruction. Up to 17% of CS abdominal images were judged to have significant blurring, which rendered them non-diagnostic.
All 18 studies we reviewed were generally enthusiastic regarding the potential of CS as a clinical tool. However, there remain important gaps in knowledge that should be addressed before CS is transitioned to routine clinical use. Only this small body of literature addresses the effects of CS on medical images, of which only a small subset examined the actual clinical diagnostic efficacy of CS MRI.
US Food and Drug Administration (FDA) guidelines for empirical evaluation of new imaging technology32 include three phases of trials through which new techniques should be evaluated: (1) exploratory/pilot (2) challenge/lab-based and (3) advanced clinical use. Based upon FDA criteria for the number of image readers and patient sample size, all of the existing literature on clinical use of CS is exploratory (1–3 image readers, 10–50 patients). FDA guidelines suggest that larger, multicentre trials of diagnostic efficacy, involving as many as 10 or more radiologists, should be completed. Given the ability to retrospectively undersample the existing medical images to simulate CS, no new images need be acquired to perform a large-scale study, which would therefore be financially and logistically feasible. However, merely increasing study size fails to address certain context-dependent obstacles, as described in the following paragraphs.
Some of the clinical CS studies reviewed here explicitly acknowledge limitations of the research that has been completed to this point. They articulate challenges that need to be overcome prior to routine clinical use and make suggestions for future research. The challenge most often noted by researchers is the difficulty of selecting parameters to optimize performance of CS.2,22,23 In the cases where this challenge has been addressed, pilot studies or multiple iterations of image reconstruction were necessary to select parameters such as the sampling pattern, regularization parameter and sparsifying transform in order to optimize results. These articles acknowledged that such a trial-and-error approach would not be possible in a clinical setting. However, since the optimal values for some parameters may be a function of the compressibility of an image, a property which varies for different anatomical areas,22 context-dependent optimization may prove essential. Sharma et al23 suggest that a standardized method for selecting these parameters must be developed before CS can be routinely implemented in clinical protocols.
Further lessons may be learnt from the research on medical image compression. The degree to which images can be successfully compressed before they no longer retain acceptable quality for diagnostic use has been referred to as compression tolerance, which is thought to be influenced by several factors such as energy distribution between low and high spectral subbands,30 SNR, the type of image contrast, pixel size and the specific organ or pathology being evaluated.40 In other words, the tolerance of an image to compression is based on the type of image and the subject of the image. While it has been demonstrated that subjective losses in image quality can occur before the diagnostic efficacy of an image is lost,41 the degree to which this is true must be established for a wide range of different types of images and pathology. It is vital that radiologists understand this context sensitivity and the potential consequences of CS reconstruction on the delineation of anatomy and detection of pathology, which may impact diagnostic performance.23
Research on imaging acceleration via PI highlights another potential gap in knowledge regarding CS: the effect of acceleration on SNR. It is known that SNR is proportional to voxel volume and to the square root of acquisition time.42 In the case of PI, an excess of SNR degradation is observed with increasing acceleration factors. This excess degradation is characterized by a geometry factor, also known as the g-factor.43 It is possible that a similar SNR-degrading factor also exists in CS MRI, a topic that warrants attention. However, SNR comparisons are only valid when voxel dimensions are fixed. Unlike PI or conventional Cartesian imaging where voxel size is given by the ratio of field of view to number of phase-encode lines (adjusted for parallel acceleration factor), this definition does not apply in CS, as is evident by the blurring artefact seen in CS images, as discussed in the section entitled “Compressed sensing artefacts”. Moreover, SNR is a function of the regularization parameter and can be made arbitrarily high: Equation (1) verifies that increase of regularization reduces the consistency of the reconstructed image with the noisy data leading to the reduction of noise in the image. Such trade of accuracy of image reconstruction for SNR via regularization has been explored in the context of PI;44,45 however, it is not essential to the PI method. Therefore, non-linear and denoising properties of CS reconstruction, which may also remove important diagnostic information, present a challenge for SNR characterization. A more promising approach is a recently developed framework for task-based assessment of image quality in CS which models clinical uses of MRI, such as identification and localization of abnormalities.46
The potential for CS to accelerate MRI acquisition with minimal effects on image quality is an exciting development for the future of radiology, and medicine as a whole. In this day of increased cognizance of healthcare costs, it is apparent that efficiency of all medical services is at a premium. This is especially true in MRI, a relatively costly and time-intensive imaging modality. Long acquisition times also limit the number of patients for whom the service is available and decrease the utility of MRI for many applications requiring high imaging speed. Thus, optimizing CS for various clinical MRI contexts is an important goal with potential to transform diagnostic imaging with respect to efficiency, cost-effectiveness and ultimately clinical utility.
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