Sparse Recovery with Partial Support and Signal Value Knowledge and Applications in Dynamic MRI

Background: Atherosclerotic renal artery stenosis (ARAS) reduces renal blood flow (RBF) and amplifies regional kidney hypoxia, but their relationship to tissue inflammation and injury markers is poorly understood. We tested the hypothesis that renal injury, reflected by renal vein levels of neutrophil gelatinase associated lipocalin (NGAL) and inflammatory cytokines monocyte chemoattractant protein-1 (MCP-1) would be magnified with severe occlusive vascular disease in humans with ARAS. Methods: Inpatient studies performed in patients with ARAS (n=40, 71.3±11% occlusion by CT angiography) or essential hypertension (EH) (n=30), during fixed Na+ intake and ACE/ARB Rx. Single-kidney cortical and medullary perfusion and RBF were measured using multidetector CT, and glomerular filtration rate (GFR) by iothalamate clearance. Tissue deoxyhemoglobin levels (R2*) and fractional kidney hypoxia (% of axial area with R2*>30/s) were measured by BOLD-MRI at 3T. Results: Single kidney RBF, cortical and medullary perfusion were reduced in the post-stenotic kidney, as was GFR. Renal vein NGAL, MCP-1 and fractional hypoxia were higher in patients with ARAS than EH. NGAL and MCP-1 levels correlated directly with cortical R2* and fractional hypoxia (r = 0.52, P <0 .0001 and r = 0.4, P = 0.0006) and with the degree of artey stenosis (r = 0.37, P = 0.04 and r = 0.35, P = 0.05). GFR correlated inversely with NGAL (r= - 0.5, P <0.0001). Conclusions: Our results demonstrate that elevated renal venous markers of kidney inflammation (MCP-1) and injury (NGAL) in ARAS are correlated with the severity of tissue hypoxia as measured by BOLD MR, suggesting a possible link between kidney inflammation and hypoxia.

MR-derived cerebral metabolic rate of oxygen utilization (CMRO(2)) has been suggested to be analogous to PET-derived CMRO(2) and therefore may be used for detection of viable tissue at risk for infarction. The purpose of this study was to evaluate MR-derived CMRO(2) mapping in acute ischemic stroke in relation to established diffusion- and perfusion-weighted imaging. In 23 patients (mean age 63 ± 18.7 years, 11 women) with imaging findings for acute ischemic stroke, relative oxygen extraction fraction was calculated from quantitative transverse relaxation times (T2, T2*) and relative cerebral blood volume using a quantitative blood oxygenation level dependent (BOLD) approach in order to detect a local increase of deoxyhemoglobin. Relative CMRO(2) (rCMRO(2)) maps were calculated by multiplying relative oxygen extraction fraction (rOEF) by cerebral blood flow, derived from PWI. After co-registration, rCMRO(2) maps were evaluated in comparison with apparent diffusion coefficient (ADC) and time-to-peak (TTP) maps. Mean rCMRO(2) values in areas with diffusion-restriction or TTP/ADC mismatch were compared with rCMRO(2) values in the contralateral tissue. In tissue with diffusion restriction, mean rCMRO(2) values were significantly decreased compared to perfusion-impaired (17.9 [95 % confidence interval 10.3, 25.0] vs. 58.1 [95 % confidence interval 50.1, 70.3]; P < 0.001) and tissue in the contralateral hemisphere (68.2 [95 % confidence interval 61.4, 75.0]; P < 0.001). rCMRO(2) in perfusion-impaired tissue showed no significant change compared to tissue in the contralateral hemisphere (58.1 [95 % confidence interval 50.1, 70.3] vs. 66.7 [95 % confidence interval 53.4, 73.4]; P = 0.34). MR-derived CMRO(2) was decreased within diffusion-restricted tissue and stable within perfusion-impaired tissue, suggesting that this technique may be adequate to reveal different pathophysiological stages in acute stroke.

Compressive sensing is a sub-Nyquist sampling technique for efficient signal acquisition and reconstruction of sparse or compressible signals. In order to account for the sparsity of the underlying signal of interest, it is common to use sparsifying priors such as Bernoulli–Gaussian-inverse Gamma (BGiG) and Gaussian-inverse Gamma (GiG) priors on the components of the signal. With the introduction of variational Bayesian inference, the sparse Bayesian learning (SBL) methods for solving the inverse problem of compressive sensing have received significant interest as the SBL methods become more efficient in terms of execution time. In this paper, we consider the sparse signal recovery problem using compressive sensing and the variational Bayesian (VB) inference framework. More specifically, we consider two widely used Bayesian models of BGiG and GiG for modeling the underlying sparse signal for this problem. Although these two models have been widely used for sparse recovery problems under various signal structures, the question of which model can outperform the other for sparse signal recovery under no specific structure has yet to be fully addressed under the VB inference setting. Here, we study these two models specifically under VB inference in detail, provide some motivating examples regarding the issues in signal reconstruction that may occur under each model, perform comparisons and provide suggestions on how to improve the performance of each model.

NMR and EPR can be combined for in vivo studies in ways that are synergistic and provide unique information. This chapter discusses the problems and advantages of combining NMR and EPR. Specific examples are given for parallel and serial experimental designs. EPR is often used to verify or calibrate the more readily available NMR methods. Examples are given of combined studies on tissue pO2 blood oxygen level dependent MR imaging (BOLD), perfusion, tissue energetics, polymer implant biochemistry, contrast agent, and studies of bioreduction.KeywordsContrast AgentBlood Oxygen Level DependentSpin TrapBlood Oxygen Level Dependent SignalSpin AdductThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Myocardial Oxygenation in Coronary Artery Disease: Insights From Blood Oxygen Level–Dependent Magnetic Resonance Imaging at 3 Tesla

Application of BOLD Magnetic Resonance Imaging for Evaluating Regional Volumetric Foot Tissue Oxygenation: A Feasibility Study in Healthy Volunteers

In this paper, we propose to apply the discrete cosine transform (DCT) and the compressive sampling (CS) techniques to audio signal compression. Using spectral analysis and the properties of the DCT, we can treat audio signals as sparse signals in the frequency domain. This is especially true for sounds representing tones. Thus, we propose the use of DCT as a preprocessor in order to sparsely represent a signal in the frequency domain, combined with CS to obtain an efficient representation of the signals. We show that the subsequent application of CS represents our signals with less information than the well-known sampling theorem.

Introduction: Blood oxygen level-dependent (BOLD) magnetic resonance imaging (MRI) during manipulation of inhaled carbon dioxide (CO₂) can be used to measure cerebrovascular reactivity (CVR) and map regions of exhausted cerebrovascular reserve. These regions exhibit a reduced or negative BOLD response to inhaled CO₂. In this study, we sought to clarify the mechanism behind the negative BOLD response by investigating its time delay (TD). Dynamic susceptibility contrast (DSC) MRI with the injection of a contrast agent was used as the gold standard in order to provide measurement of the blood arrival time to which CVR TD could be compared. We hypothesize that if negative BOLD responses are the result of a steal phenomenon, they should be synchronized with positive BOLD responses from healthy brain tissue, even though the blood arrival time would be delayed. Methods: On a 3-tesla MRI system, BOLD CVR and DSC images were collected in a group of 19 patients with steno-occlusive cerebrovascular disease. For each patient, we generated a CVR magnitude map by regressing the BOLD signal with the end-tidal partial pressure of CO₂ (P_ETCO₂), and a CVR TD map by extracting the time of maximum cross-correlation between the BOLD signal and P_ETCO₂. In addition, a blood arrival time map was generated by fitting the DSC signal with a gamma variate function. ROI masks corresponding to varying degrees of reactivity were constructed. Within these masks, the mean CVR magnitude, CVR TD and DSC blood arrival time were extracted and averaged over the 19 patients. CVR magnitude and CVR TD were then plotted against DSC blood arrival time. Results: The results show that CVR magnitude is highly correlated to DSC blood arrival time. As expected, the most compromised tissues with the longest blood arrival time have the lowest (most negative) CVR magnitude. However, CVR TD shows a noncontinuous relationship with DSC blood arrival time. CVR TD is well correlated to DSC blood arrival time (p < 0.0001) for tissue of positive reactivity, but fails to maintain this trend for tissue of negative reactivity. Regions with negative reactivity have similar CVR TD than healthy regions. Conclusion: These results support the hypothesis that negative reactivity is the result of a steal phenomenon, lowering the BOLD signal as soon as healthier parts of the brain start to react and augment their blood flow. BOLD CVR MRI is capable of identifying this steal distribution, which has particular diagnostic significance as it represents an actual reduction in flow to already compromised tissue.

Background: Renal hypoxia is a complex function of post-glomerular medullary blood flow, active solute transport and is considered a major risk element for acute kidney injury. Previous studies indicate that sodium balance, diuretic administration and some drugs affect tissue oxygenation. Water loading in younger subjects lowers medullary deoxyhemoglobin. We sought to evaluate the effects of water loading on the day of BOLD imaging in older subjects undergoing protocol evaluation of atherosclerotic renovascular disease (ARVD). METHODS: Inpatient studies were performed in patients with hemodynamically severe ARVD (n=15, Doppler US velocity &gt;270 cm/sec), during 150 mEq Na+ intake and ACE/ARB Rx. Two groups were studied: Group A (n=10) received oral water loading (20 ml/kg), whereas Group B (n=5) had none. Tissue R2* (index of deoxyhemoglobin levels) and fractional kidney hypoxia (medullary estimate) (% of renal coronal area with R2*&gt;20/s) were measured in stenotic kidneys by BOLD-MRI at 3T, before and after IV injection of Furosemide (20gm). RESULTS: Cortical R2* and fractional tissue hypoxia were similar for the 2 groups (P =0.6 and 0.7). Both groups reduced cortical R2* and fractional hypoxia after furosemide injection to the same degree. Table CONCLUSION: These data demonstrate that water loading on the day of BOLD evaluation in older subjects with ARVD does not materially alter cortical or medullary estimates of oxygenation. Our results extend previous studies indicating that water loading in older individuals fails to alter medullary oxygenation unlike alterations in sodium intake, diuretic administration or blockade of the renin-angiotensin system.

Gradient Immune-based Sparse Signal Reconstruction Algorithm for Compressive Sensing

We present an expansion-compression variance-component based method (EXCOV) for reconstructing sparse or compressible signals from noisy measurements. The measurements follow an underdetermined linear model, with noise covariance matrix known up to a constant. To impose sparse or compressible signal structure, we define high- and low-signal coefficients, where each high-signal coefficient is assigned its own variance, low-signal coefficients are assigned a common variance, and all the variance components are unknown. Our expansion-compression scheme approximately maximizes a generalized maximum likelihood (GML) criterion, providing an approximate GML estimate of the high-signal coefficient set and an empirical Bayesian estimate of the signal coefficients.We apply the proposed method to reconstruct signals from compressive samples, compare it with existing approaches, and demonstrate its performance via numerical simulations.

As an alternative paradigm to the Shannon-Nyquist sampling theorem, compressive sensing enables sparse signals to be acquired by sub-Nyquist analog-to-digital converters thus may launch a revolution in signal collection, transmission and processing. In the practical compressive sensing applications, the sparse signal is always affected by noise and interference, and therefore the recovery performance reduces based on the conventional compressive sensing, especially in the low signal-to-noise scene, the sparse recovery is usually unavailable. In this paper, the influence of noise on recovery performance is analyzed, so as to provide the theoretical basis for the noise folding phenomenon in compressive sensing. From the analysis, we find that the expected noise gain in the random measure process is closely related to the row and column of the measurement matrix. However, only those columns corresponding to the support for the sparse signal contribute to the sparse vector. In the traditional Shannon-Nyquist sampling system, an antialiasing filter is applied before the sampling process, so as to filter the noise beyond the passband of interest. Inspired by the necessity of antialiasing filtering in bandpass signal sampling, we propose a selective measurement scheme, namely adapted compressive sensing, whose measurement matrix can be updated according to the noise information fed back by the processing center. The measurement matrix is specially designed, and the sensing matrix has directivity so that the signal noise can be suppressed. The measurement matrix senses only the spectrum of interest, where the sparse spectrum is most likely to lie. Moreover, we compare the recovery performance of the proposed adaptive scheme with those of the non-adaptive orthogonal matching pursuit algorithm, FOCal underdetermined system solver algorithm, and sarse Bayesian learning algorithm. Extensive numerical experiments show that the proposed scheme has a better improvement in the performance of the sparse signal recovery. From the viewpoint of implementation, the measurement noise should be taken into consideration in the system, and more efficient algorithms will be developed for source pre-estimation at lower signal-to-noise ratio.

To prospectively assess the oxygenation state of renal transplants and determine the feasibility of using blood oxygen level-dependent (BOLD) magnetic resonance (MR) imaging to differentiate between acute tubular necrosis (ATN), acute rejection, and normal function. This HIPAA-compliant study had institutional human subjects review committee approval, and written informed consent was obtained from all patients. BOLD MR imaging was performed in 20 patients (age range, 21-70 years) who had recently received renal transplants. Six patients had clinically normal functioning transplants, eight had biopsy-proved rejection, and six had biopsy-proved ATN. R2* (1/sec) measurements were obtained in the medulla and cortex of transplanted kidneys. R2* is a measure of the rate of signal loss in a specific region and is related to the amount of deoxyhemoglobin present. Statistical analysis was performed by using a two-sample t test. Threshold R2* values were identified to discriminate between transplanted kidneys with ATN, those with acute rejection, and those with normal function. R2* values for the medulla were significantly lower in the acute rejection group (R2* = 15.8/sec +/- 1.5) than in normally functioning transplants (R2* = 23.9/sec +/- 3.2) and transplants with ATN (R2* = 21.3/sec +/- 1.9). The differences between the acute rejection and normal function groups (P = .001), as well as between the acute rejection and ATN groups (P < .001), were significant. Acute rejection could be differentiated from normal function and ATN in all cases by using a threshold R2* value of 18/sec. R2* values for the cortex were higher in ATN (R2* = 14.2/sec +/- 1.4) than for normally functioning transplants (R2* = 12.7/sec +/- 1.6) and transplants with rejection (R2* = 12.4/sec +/- 1.2). The difference in R2* values in the cortex between ATN and rejection was statistically significant (P = .034), although there was no threshold value that enabled differentiation of all cases of ATN from cases of normal function or acute rejection. R2* measurements in the medullary regions of transplanted kidneys with acute rejection were significantly lower than those in normally functioning transplants or transplants with ATN. These results suggest that marked changes in intrarenal oxygenation occur during acute transplant rejection.

Compressive sensing (CS) is one of the effective data compression methods where a small number of measurements of a sparse signal is required to have an exact recovery. In Compressive sensing technique, the data is acquired and compressed at the same time. CS concept allows capturing only fewer sparse and compressible signal which contains only useful information that helps to recover a proper signal. In this paper, image compression is performed with compressive sensing concept. The different basis matrices and sensing matrices are considered which satisfy the Restricted Isometric Property (RIP) and Independent and Identically Distributed (IID). The hardware implementation of CS is covered to have real-time compression for various image-based applications. The performance is observed regarding SNR, compression ratio, and correlation. The reconstruction algorithms are implemented on MATLAB platform. The obtained results show satisfactory performance for CS based image compression.

The recently introduced Compressed Sensing (CS) theory explains how sparse or compressible signals can be reconstructed from far fewer samples than what was previously believed possible. The CS theory has attracted significant attention for applications such as Magnetic Resonance Imaging (MRI) where long acquisition times have been problematic. This is especially true for dynamic MRI applications where high spatio-temporal resolution is needed. For example, in cardiac cine MRI, it is desirable to acquire the whole cardiac volume within a single breath-hold in order to avoid artifacts due to respiratory motion. Conventional MRI techniques do not allow reconstruction of high resolution image sequences from such limited amount of data. Vaswani et al. recently proposed an extension of the CS framework to problems with partially known support (i.e. sparsity pattern). In their work, the problem of recursive reconstruction of time sequences of sparse signals was considered. Under the assumption that the support of the signal changes slowly over time, they proposed using the support of the previous frame as the "known" part of the support for the current frame. While this approach works well for image sequences with little or no motion, motion causes significant change in support between adjacent frames. In this paper, we illustrate how motion estimation and compensation techniques can be used to reconstruct more accurate estimates of support for image sequences with substantial motion (such as cardiac MRI). Experimental results using phantoms as well as real MRI data sets illustrate the improved performance of the proposed technique.