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Monte Carlobased noise compensation in coil intensity corrected endorectal MRI
 Dorothy Lui^{1},
 Amen Modhafar^{1},
 Masoom A. Haider^{2} and
 Alexander Wong^{1}Email author
Received: 10 December 2014
Accepted: 15 September 2015
Published: 12 October 2015
Abstract
Background
Prostate cancer is one of the most common forms of cancer found in males making early diagnosis important. Magnetic resonance imaging (MRI) has been useful in visualizing and localizing tumor candidates and with the use of endorectal coils (ERC), the signaltonoise ratio (SNR) can be improved. The coils introduce intensity inhomogeneities and the surface coil intensity correction built into MRI scanners is used to reduce these inhomogeneities. However, the correction typically performed at the MRI scanner level leads to noise amplification and noise level variations.
Methods
In this study, we introduce a new Monte Carlobased noise compensation approach for coil intensity corrected endorectal MRI which allows for effective noise compensation and preservation of details within the prostate. The approach accounts for the ERC SNR profile via a spatiallyadaptive noise model for correcting nonstationary noise variations. Such a method is useful particularly for improving the image quality of coil intensity corrected endorectal MRI data performed at the MRI scanner level and when the original raw data is not available.
Results
SNR and contrasttonoise ratio (CNR) analysis in patient experiments demonstrate an average improvement of 11.7 and 11.2 dB respectively over uncorrected endorectal MRI, and provides strong performance when compared to existing approaches.
Discussion
Experimental results using both phantom and patient data showed that ACER provided strong performance in terms of SNR, CNR, edge preservation, subjective scoring when compared to a number of existing approaches.
Conclusions
A new noise compensation method was developed for the purpose of improving the quality of coil intensity corrected endorectal MRI data performed at the MRI scanner level. We illustrate that promising noise compensation performance can be achieved for the proposed approach, which is particularly important for processing coil intensity corrected endorectal MRI data performed at the MRI scanner level and when the original raw data is not available.
Background
Prostate cancer (PCa) is one of the most commonly diagnosed cancers among North American men, encompassing an estimated 14 % and 24 % of all new cancer cases in the United States and Canada respectively. In 2014, an estimated 233,000 American and 23,600 Canadian men are expected to be diagnosed with PCa and of those cases, 29,480 and 4,000 are expected to result in death [1, 2]. Prostate specific antigen (PSA) blood assay and digital rectal exams are exams used for screening PCa. High PSA levels indicate high PCa risk. The use of PSA is controversial and often inadequate as it overdetects clinically insignificant prostate cancer, resulting in a high degree of overtreatment. Treatment of prostate cancer with radiation or surgery carries significant risk of life altering side effects such as sexual dysfunction, urinary and rectal incontinence and thus should not be undertaken unless necessary [3, 4]. After a positive screening, the next step is systematic transrectal ultrasound (TRUS) guided biopsy which involves systematic regional sampling of the prostate with typically 8 or more samples being taken. This is invasive and uncomfortable and suffers from sampling error as the tumors are not easily visible with TRUS. As such, it is important to consider detection alternatives. Magnetic Resonance Imaging (MRI) has been shown to be a viable alternative as it can visualize the cancer and has a good negative predictive value for significant cancer, helping avoid unnecessary biopsy and reduction of sampling error.
MRI has become a commonly used diagnostic imaging tool for detecting PCa due to its improved contrast between cancer and background healthy tissue in a tomographic view. Better signaltonoise ratio (SNR) can be achieved using a localized surface receiver coil placed directly over the body region of interest (ROI) to increase the magnetic sensitivity. Placed on the skin surface, these surface coils are relatively far from the centrally located prostate (i.e. >10 cm). Alternatively, endorectal coils (ERCs) placed in the rectum are within a few millimeters of the prostate gland. With both surface and ERCs, the signal decreases farther away from the coil and consequently introduces intensity inhomogeneities. ERCs have recently been shown to offer a diagnostic advantage [5] in the detection of prostate cancer compared to surface coils at 3 T. As such, there remains a strong interest in utilizing ERC despite the discomfort associated with insertion of the endorectal balloon. For lower field systems operating at 1.5 T, an ERC is helpful in achieving significant improved SNR (10fold) [6] and performance that is superior to 3 T MRI with phasedarray coils (PAC) [7]. The results demonstrated no significant visualization difference between the two approaches, although according to Beyersdorff et al. [7] ERCs exhibited improved SNR. Thus, the use of ERCs remains a particular interest at 1.5 T as well. Conversely, the ERC’s inhomogeneous sensitivity results in high intensities at the prostate’s peripheral zone nearest the coil and decreases in intensity near the upper region of the central gland, making visualization, delineation and diagnosis difficult [8].
MRI noise is an issue under active research [11, 12]. It amounts to difficult analysis and hinders postprocessing approaches such as segmentation and registration [13–18]. Raw MRI data is complex (both real and imaginary components) and represented in the frequency domain with additive Gaussian noise. Transforming this complex data to the spatial domain renders the magnitude data to be Rician distributed [14, 19, 20]. The data distribution is also dependent upon the SNR, where low SNR regions (mainly described by noise only) can be modeled as Rayleigh distributed [20, 21] and high SNR regions as Gaussian distributed [14, 20, 22]. Moreover, the signaldependent nature of noise in the intensity corrected images introduces challenges to noise compensation.
Taking the characteristic distributions of MRI data into consideration, noise can be compensated. Numerous approaches have been proposed using MRI magnitude data to compensate for noise, using a variety of methods including total variation [23–25], analyzing multiple scales using wavelet denoising [26–28], via nonlocal means [13, 22, 29–31] and linear minimum meansquare estimators (LMMSE) [14, 32]. These approaches combine a mixture of techniques to handle the particular nature of MRI noise: spatialadaptation to the noise variance [11, 24, 29, 33], Rician distribution [24, 25, 28, 29, 34] and accounting for signaldependent bias when using a Gaussian assumption [11, 27–29].
In this study, a new approach called Adaptive Coil Enhancement Reconstruction (ACER) is introduced that is suitable for coil intensity corrected endorectal MR images. ACER reconstructs noisecompensated endorectal MR magnitude images using a stochastic Bayesian estimation framework. A spatiallyadaptive Monte Carlo sampling approach is introduced to estimate the posterior distribution using a Rician model. The Monte Carlo posterior estimation is modified to model the Riciannature of MRI magnitude data. Moreover, the SNR profile of the specific ERC used is incorporated into the posterior estimation by integrating a learned parametric nonstationary Rician model. The model is learned using maximum likelihood estimation based on the data and specifications of the ERC. The posterior estimate is then used to form a noisesuppressed reconstruction using Bayesian leastsquares estimation. Given the pressures of acquiring MRI data more quickly, the proposed approach offers an alternative to obtain increased SNR by postprocessing retrospective coil intensity corrected data for improved visualization.
Methods
In this section, the problem is formulated and the process of how the noisecompensated image is reconstructed is discussed.
Problem formulation
In Eq. 5, G(s) can be estimated using the conditional mean of G(s) on V(s), E(G(s)V(s)), or the mean of the posterior distribution, p(G(s)V(s)). An estimate of the posterior distribution, p(G(s)V(s)), can be calculated using a spatiallyadaptive importanceweighted MonteCarlo sampling approach. The approach is adapted to account for the nonstationary Rician characteristics of MRI magnitude data. This is explained in more detail in the next section.
Spatiallyadaptive Rician distributed Monte Carlo Posterior estimation
where δ() is the Dirac delta function and Z is a normalization term to enforce \(\int \hat {p}(G_{j}V_{j}) = 1\). The posterior distribution can then be used to calculate the noisecompensated reconstruction \(\hat {G}(s)\) using Eq. 5.
Nonstationary unified ERC parametric model
where x are the observed intensities in V(s) and θ are the parameters to be estimated: in this case, the scale parameter, \(\hat {\Phi }(s_{0})\). To refine the scale estimation, an existing SNR profile, defined as γ(θ), which is characteristic to a given ERC, is fitted. Given an ERC, an SNR profile can be mapped to characterize the change in SNR as a function of distance from the ERC surface. Literature has shown that the ERC SNR profile differs from a rigid and inflatable coil, however both coils share a common trend where there is an SNR gain nearest the coil surface which diminishes with distance [40–42]. Considering the SNR depth profile from posterior to anterior of a rigid coil, a sharp increase in SNR of 3 to 5 times the normal SNR is demonstrated at the ERC surface. This increase is followed by a decrease through the peripheral zone and central gland. Despite the quick decline in SNR, the peripheral zone still experiences a gain in SNR of 1.5 to 3 times. The continual decrease then finds the central gland with only a fraction of the SNR [40–42]. An inflatable coil has demonstrated a weaker response with less SNR increase near the coil. In addition to the variation between SNR profiles for inflatable and rigid ERC, ERC brands have their own characteristic profiles which can be determined by measuring phantoms. Two SNR profiles were modeled in this study using the findings from Venugopal et al. [40] for two ERCs: a Hologic rigid ERC and a Medrad inflatable ERC. The inflatable and rigid ERC SNR profiles demonstrate a 1 and 5fold improvement in SNR at the ERC surface respectively with an exponential drop leading to a final abrupt drop. The full algorithm, Adaptive Coil Enhancement Reconstruction (ACER), is summarized in Algorithm 1.
Experiments
To interpret the performance of the proposed approach, clinical patient data and phantom data were used. Clinical patient and phantom endorectal T2 (spinspin relaxation time) and axial diffusionweighted MRI (DWI) corrected with the precalibration coil intensity correction approach by GE called Phased array UnifoRmity Enhancement (PURE) was collected at Sunnybrook Health Sciences Center. Two types of coils were used to acquire the data: an inflatable Medrad eCoil ERC and a rigid Hologic ERC. The data was collected using a GE Discovery MR750 3 T MRI for phantom data (inflatable coil only) and a GE Signa HDxt 1.5 T MRI for patient data (collected with both rigid and inflatable ERCs).
The proposed approach was compared against three other MRI denoising approaches: 1.) an optimized variancestabilizing transformation for Rician distributions (ROVST) [19], 2.) noise removal by a multiresolution adaptive nonlocal means approach (ANLM) [29] and 3.) a linear minimum mean squared error estimator (LMMSE) [32]. The ROVST, LMMSE and ANLM codes used for comparison were provided by their respective authors. All approaches were implemented using MATLAB and the parameters were selected to provide a reasonable balance between prostate detail and noise compensation in the background. The experimental setup for the phantom and patient experiments are described in more detail in the following sections.
Phantom experimental setup
For phantom experiments, a multimodality prostate training phantom from Computerized Imaging Reference Systems Inc (CIRCS Model 053) was used. The phantom is contained within a 12×7.0×9.5 cm clear container made of acrylic. The container has two openings for the probe (front  3.2 cm diameter and rear  2.6 cm diameter). Located inside the container is a prostate replica composed of high scattering Blue Zerdine (5.0×4.5×4.0 cm) that is placed in a waterlike background gel with little backscatter attenuation (≤0.07 dB/cmMHz). Within the prostate itself, there are three 0.5−1.0 cm lesions placed hypoechoic to the prostate. The urethra and rectal wall are made of low scattering Zerdine with diameter of 0.70 cm and dimensions 6.0×11×0.5 cm respectively.
Phantom endorectal T2 data collection protocol
Parameter  Setting 

Coil  Medrad eCoil ERC 
NEX  1 
TE  107 ms 
TR  3,200 ms 
DFOV  16×16 cm 
pixel spacing  0.3 mm 
slice thickness  3 mm 
Clinical endorectal DWI data collection protocol
Parameter  Setting 

Coil  Medrad eCoil ERC 
bvalues  0 s/ mm^{2}, 1000 s/ mm^{2} 
NEX  1 
TE  72 ms 
TR  10,000 ms 
DFOV  16×16 cm 
pixel spacing  0.6 mm 
slice thickness  3 mm 
Patient experimental setup
Clinical endorectal T2 data collection protocol
Parameter  Setting 

NEX  0.5 
TE  100 – 107 ms (median: 104 ms) 
TR  3,400 ms 
DFOV  16×16 cm 
pixel spacing  0.3 mm 
slice thickness  3 mm 
Results and discussion
Following the experimental setup, a number of quantitative and qualitative analysis methods were executed to evaluate the performance of the proposed approach against the stateoftheart techniques.
Phantom experiment
For the phantom experiments, the noise suppression approaches were compared using signaltonoise ratio (SNR), contrasttonoise ratio (CNR) and visual analysis. Pvalues were also calculated to determine the statistical significance of the SNR and CNR results. The null hypothesis used was that the proposed ACER approach had no improvement for a subjective metric as compared to a given correction approach. Pvalues were calculated for a twotailed normal distribution with a statistical significance level of 5 %.
In the SNR equation, the parameter, \(\bar {x}\), defines the mean value of the region and σ signifies the standard deviation of the region. The SNR metric used in this study is based on the regionofinterest (ROI) approach commonly used in clinical practice [43, 44]. In CNR, \(\bar {x}_{A}\) and \(\bar {x}_{B}\), denote the mean values of the selected background and prostate regions respectively and σ is the standard deviation of the background region which is more indicative of the noise process.
Phantom SNR analysis of a selected prostate region (in dB with highest measures in bold). ACER proved to have the greatest SNR improvement in the prostate regions. ANLM showed an inaccurate noise variance estimate which led to less significant SNR improvement
Case  ACER  ROVST  LMMSE  ANLM  UC 

D W I _{b=0}  27.0  26.8  26.7  26.2  26.1 
D W I _{b=1000}  27.3  27.5  26.9  25.9  25.7 
T2  27.2  26.7  26.9  26.7  26.7 
Avg./Std.  27.2/0.15  27.0/0.43  26.8/0.12  26.3/0.40  26.2/0.50 
Phantom SNR analysis of a selected background region (in dB with highest measures in bold). ACER proved to have the greatest SNR improvement in the background regions. ANLM showed an inaccurate noise variance estimate which led to less significant SNR improvement
Case  ACER  ROVST  LMMSE  ANLM  UC 

D W I _{b=0}  33.2  32.0  31.6  30.9  30.6 
D W I _{b=1000}  27.5  27.6  26.4  26.0  25.9 
T2  29.2  27.0  27.6  27.0  26.9 
Avg./Std.  30.0/2.9  28.9/2.7  28.5/2.7  27.9/2.6  27.8/2.5 
Phantom CNR analysis based on the selected background and prostate regions (in dB with highest measures in bold). ACER demonstrated the greatest improvement in CNR illustrating its capacity to augment the detail within the prostate
Case  ACER  ROVST  LMMSE  ANLM  UC 

D W I _{b=0}  27.1  25.9  25.4  24.7  24.5 
D W I _{b=1000}  20.9  21.0  19.7  19.4  19.4 
T2  19.7  17.6  18.1  17.5  17.5 
Avg./Std.  22.6/3.9  21.5/4.1  21.1/3.8  20.5/3.7  20.4/3.6 
CNR analysis (Table 6) showed that ACER had the highest average CNR. ROVST had the second highest average CNR and ANLM with the least improvement. These results indicate ACER’s ability to increase the contrast between the background and prostate regions, thereby improving the visibility of detail within the prostate.
The pvalues for the metrics measured for the phantom experiments compared to the proposed ACER method. Values below 0.05 are shown bolded which indicate the average score across the cases has statistical significance
Metric  UC  ROVST  LMMSE  ANLM 

SNR  0.004  0.15  0.02  0.005 
CNR  0.02  0.23  0.01  0.02 
The noise suppressed T2 phantom slices for each approach are shown in Fig. 3. The proposed method demonstrates the best noise compensation while enhancing the detail contrast within the prostate. LMMSE and ROVST also compensate for noise however at the cost of visible structure and edge blurring.
Patient experiment
The noise suppression approaches were then compared using patient data by analyzing SNR, CNR (Eq. 11), edge preservation (Eq. 12) and subjective scores. Pvalues were also calculated to determine the statistical significance of the SNR and CNR results. Here, the null hypothesis used was that a given approach had no improvement for a subjective metric as compared to the uncorrected image. Pvalues were calculated for a twotailed normal distribution with a statistical significance level of 5 %.
The patient experiment SNR of a background region are shown (largest values are shown in bold). ACER demonstrates an average increase of 11.7 dB for SNR over the uncorrected (UC) slice which has no noise suppression applied
Case  ACER  ROVST  LMMSE  ANLM  UC 

1  34.2  22.6  31.5  23.1  19.4 
2  26.8  21.7  25.7  21.1  18.5 
3  33.1  34.7  32.2  26.6  19.6 
4  32.3  36.3  34.8  27.7  20.2 
5  34.1  33.4  32.5  26.7  22.1 
6  34.8  31.6  33.1  26.5  19.9 
7  34.1  33.2  33.3  25.7  22.3 
8  32.6  36.2  33.9  27.3  19.5 
9  33.6  35.0  34.5  27.4  19.6 
10  34.0  37.0  35.7  27.6  19.6 
11  33.0  27.9  25.4  21.0  13.8 
12  26.5  23.5  20.3  20.1  13.2 
13  28.1  28.2  19.0  22.3  13.3 
14  22.8  24.9  20.4  21.4  13.7 
15  25.9  23.9  18.4  20.7  13.2 
16  25.4  25.6  21.5  21.5  14.1 
17  24.8  25.7  19.6  21.4  13.4 
18  19.2  13.1  16.8  15.0  12.8 
19  18.7  13.3  16.0  15.5  12.6 
20  12.9  11.9  13.8  13.0  11.7 
Avg./Std.  28.3/6.1  27.0/7.6  25.9/7.3  22.6/4.3  16.6/3.5 
The patient experiment CNR of two regions are shown (largest values are shown in bold). ACER demonstrates an average increase of 11.2 dB for CNR over the uncorrected (UC) slice which has no noise suppression applied
Case  ACER  ROVST  LMMSE  ANLM  UC 

1  37.0  25.3  34.5  25.8  22.1 
2  31.3  26.2  30.7  25.7  23.0 
3  36.1  37.7  35.3  29.6  22.6 
4  30.6  34.6  33.3  26.0  18.4 
5  29.1  28.4  27.6  21.7  17.2 
6  30.9  27.9  29.5  22.7  16.1 
7  33.6  32.7  32.9  25.2  21.8 
8  35.6  39.2  37.0  30.3  22.5 
9  34.6  36.0  35.7  28.5  20.7 
10  33.0  36.2  35.1  26.7  18.8 
11  36.1  41.0  39.2  34.0  26.8 
12  26.8  23.8  20.7  20.4  13.5 
13  24.8  24.9  15.9  19.0  10.0 
14  22.3  24.5  20.3  21.1  13.4 
15  26.6  24.6  19.4  21.4  13.8 
16  24.7  24.9  21.2  20.9  13.5 
17  24.0  25.0  19.3  20.7  12.6 
18  17.9  11.7  15.5  13.6  11.4 
19  18.3  12.8  15.7  15.1  12.2 
20  10.6  9.5  11.5  10.6  9.3 
Avg./Std.  28.2/6.9  27.3/8.6  26.5/8.5  22.9/5.6  17.0/4.9 
The pvalues for the metrics measured for the patient experiments. Values below 0.05 indicate the average score for all slices corrected by each approach represents statistically significant change from the uncorrected slices. All approaches have pvalues below 0.05
Metric  ACER  ROVST  LMMSE  ANLM 

SNR  4.56E11  1.30E07  8.96E09  8.93E10 
CNR  1.54E11  1.30E07  5.99E09  8.88E10 
where ▽^{2}V and \(\bigtriangledown ^{2}\hat G\) are the Laplacian of the intensity bias corrected image and noisefree reconstruction respectively using a 3×3 filter. The parameters, \(\overline {\bigtriangledown ^{2}V}\) and \(\overline {\bigtriangledown ^{2}\hat G}\), are the mean values of a neighbourhood around ▽^{2}V and \(\bigtriangledown ^{2}\hat G\). An image where there is perfect EP results in a measurement of Υ=1. This refers to the technique’s ability to retain the structure and edges of the image. For the purpose of this study, since noise can be recognized as edges or details, the EP metric is calculated for the prostate gland only using a user defined mask. This region was selected for high SNR and high importance for detail preservation.
Patient experiment edge preservation results: ANLM has the highest average edge preservation (EP) metrics as a result of insufficient noise suppression. ROVST and LMMSE demonstrate lower average metrics as a result of overcompensation. ACER defines an optimal balance between noise suppression and edge preservation which enhances visualization with the second highest EP metrics
Case  ACER  ROVST  LMMSE  ANLM 

1  0.977  0.994  0.982  1.000 
2  0.936  0.982  0.954  0.996 
3  0.953  0.875  0.932  0.979 
4  0.956  0.840  0.847  0.954 
5  0.846  0.832  0.836  0.957 
6  0.933  0.881  0.907  0.980 
7  0.895  0.884  0.890  0.979 
8  0.971  0.863  0.930  0.975 
9  0.896  0.861  0.881  0.963 
10  0.954  0.869  0.903  0.976 
11  0.923  0.792  0.938  0.973 
12  0.970  0.867  0.872  0.981 
13  0.960  0.896  0.902  0.984 
14  0.985  0.923  0.921  0.987 
15  0.935  0.838  0.860  0.969 
16  0.952  0.868  0.868  0.978 
17  0.973  0.903  0.906  0.984 
18  0.957  0.986  0.957  0.999 
19  0.980  0.993  0.981  1.000 
20  0.974  0.992  0.971  1.000 
Avg./Std.  0.946/0.03  0.897/0.05  0.912/0.04  0.981/0.01 
Image analysis and subjective interpretation

MH, 16 years of clinical radiology experience with specialization in genitourinary cancers and 11 years of experience interpreting prostate MRI

LM, 7 years of clinical radiology experience with specialization in cancer imaging

FK, 5 years of prostate MRI research experience

HC, 1.5 years of clinical radiology experience

AM, 1.5 years of clinical imaging research experience

JK, 2 months of clinical prostate MRI experience

KC, 50 hours of clinical prostate MRI experience
The rank sum subjective score values (with highest scores shown in bold): ACER has the highest rank sum for contrast and lack of noise
Scoring Criterion  ACER  ROVST  LMMSE  ANLM  UC 

Contrast  63  61  47  60  62 
Sharpness  58  48  21  65  68 
Lack of noise  80  76  76  72  62 
Fitness for purpose  70  54  27  70  65 
The median subjective score values (with the highest scores shown in bold): ACER and ANLM demonstrated the same median scores as UC except for lack of noise where all approaches improved upon UC
Scoring Criterion  ACER  ROVST  LMMSE  ANLM  UC 

Contrast  3  3  2  3  3 
Sharpness  3  2  1  3  3 
Lack of noise  4  4  4  4  3 
Fitness for purpose  3  2  1  3  3 
The Fpseudosigma subjective score values (with the lowest scores shown in bold): With the exception of the unanimous decision that LMMSE had poor sharpness, most of the criteria for the approaches had high variance indicating large inconsistencies in opinion implying that personal preference has a large impact upon the approach
Scoring Criterion  ACER  ROVST  LMMSE  ANLM  UC 

Contrast  0.37  0.74  0.74  0.74  1.48 
Sharpness  0.93  0.74  0.00  0.93  0.93 
Lack of noise  0.93  0.93  1.48  0.74  0.19 
Fitness for purpose  0.93  0.74  0.74  0.74  1.48 
where N is the number of evaluators and M is the number of slices evaluators evaluated and S_{ ij } are the individual scores of each evaluator for each slice. The total rank sum can then be used to determine whether in general the evaluators decided a particular criterion was high or low for a given approach.
where IQR is the interquartile range. A smaller Fpseudosigma denotes a more precise score.
Considering the histograms (Fig. 7), rank sum (Table 12), median (Table 13) and Fpseudosigma (Table 14) metrics for contrast, ACER had the highest rank sum with a median score of satisfactory. It also had the smallest Fpseudosigma which indicates there was little variation between all scores. For the sharpness criterion, it was interesting that the uncorrected image had the largest rank sum with ANLM having the next highest rank sum. ACER, ANLM and uncorrected tied with the highest median scores of satisfactory however also had the highest Fpseudosigmas indicating large variation in opinion. It was unanimous however that LMMSE had very poor sharpness and was found to be less sharp than the uncorrected slices. For the lack of noise criterion, ACER again had the largest rank sum with a median score of good. All correction approaches had high rank sums and median scores of good however again, Fpseudosigmas hinted at large variance in opinion. This may have been caused by the large number of evaluators and the variance in noise level between cases. Finally, ACER and ANLM had the highest rank sums for fitness for purpose with a median score of satisfactory. LMMSE and ROVST were found to be unfit for the purpose in comparison to uncorrected slices. It is intriguing to point out that evaluators found that the uncorrected slices were just as sufficient for analysis as ACER and ANLM however there was large variance in opinion with large Fpseudosigma scores.
Visual analysis
Timing analysis
Computation times for each approach on the real T2 endorectal MRI shown in seconds. Shortest computation times are shown bolded. LMMSE had the shortest average computation time with 0.13 s while ANLM had the longest average computation time with 1060 s
Case  ACER  ROVST  LMMSE  ANLM 

1  370  9.82  0.17  1170 
2  265  8.22  0.12  1090 
3  256  8.33  0.13  1310 
4  270  8.43  0.13  1340 
5  268  8.47  0.11  1310 
6  274  8.34  0.12  1280 
7  299  8.32  0.12  1330 
8  361  8.43  0.13  1330 
9  295  8.5  0.12  1240 
10  285  8.42  0.12  1210 
11  272  8.31  0.12  1210 
12  276  7.22  0.19  923 
13  275  6.99  0.11  888 
14  274  6.85  0.12  848 
15  273  7.03  0.12  846 
16  273  6.99  0.12  789 
17  272  7.06  0.14  871 
18  272  7.28  0.13  753 
19  272  7.34  0.14  693 
20  273  7.28  0.12  690 
Avg./Std.  284/28.7  7.88/0.77  0.13/0.01  1060/234.7 
Conclusion
In this study, a novel noise compensation approach for coil intensity corrected endorectal MRI images is presented. Adaptive Coil Enhancement Reconstruction (ACER) uses a spatiallyadaptive Monte Carlo sampling approach to estimate the Riciandistributed posterior in MRI images to reconstruct the noise compensated image. ACER takes advantage of the known SNR characteristics of an ERC to develop a nonspatial unified ERC parametric model that models the SNR profile presented by the ERC. This allows for effective noise suppression and detail preservation in the prostate. This approach to noise compensation for coil intensity corrected endorectal MRI images is particularly useful for retrospective studies where the original raw data is not available and only the coil intensity corrected data is accessible. Experimental results using both phantom and patient data showed that ACER provided strong performance in terms of SNR, CNR and edge preservation when compared to a number of existing approaches. Future work involves extending ACER to automatically estimate the SNR profile of the ERC, thus eliminating the necessity for the ERC SNR profile, investigating the effect and efficacy of ACER on improving the quality of multisequence endorectal modalities such as correlated diffusion imaging [47], as well as investigating the extension of ACER for endorectal compressed sensing MRI [48]. Furthermore, as future work it would be of great interest to perform a more comprehensive study in the effects of noise compensation on resolution, as well as utilize other metrics for quality assessment such as signaltonoise ratio computed based on multiple acquisitions for a more thorough assessment of image quality.
Declarations
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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