Regression error estimation significantly improves the region-of-interest statistics of noisy MR images

Vladimir Juras, Štefan Zbýň, Pavol Szomolanyi, Siegfried Trattnig

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Purpose: The region-of-interest (ROI) selection and evaluation is one of the key factors in the successful evaluation of radiological images. However, the presence of noise in images may lead to incorrect diagnosis. The aim of this study was to test the hypothesis that the weighting by error estimation in ROI assessment might significantly improve the validity of the results. Methods: As a model, the data maps of the transverse relaxation time constants (T 2) from patients who underwent a matrix-associated chondrocyte transplantation procedure on the femoral condyle were analyzed. Artificial noise with a Rician density probability distribution was added to each TE image. ROIs were processed either as a regular arithmetic mean or as a weighted mean, in which weighted coefficients were calculated with regard to fitting error estimates [coefficient of determination (R2); root mean squared error (RMSE), mean absolute error (MSE), mean squared error (MAE), and chi-squared error (χ2)]. Results: The global T2 values in repair tissue (mean±standard deviation, 62±7 ms; range 51-70 ms) and in healthy cartilage (mean±SD, 49±6 ms; range 40-60 ms) were significantly different (p<0.001). With a 45% or greater decrease from the original SNR value (corresponding to a noise level of 35% of random value), the statistical significance was lost (P>0.05); however, the use of the coefficient of determination (R2) as a correction factor was able to maintain the p-value of <0.05 up to a 56% decrease from the original SNR value. Conclusions: The results of this study can prospectively be applied in a wide range of radiological imaging techniques in cases when error estimation is possible. Our analysis on MR images with artificially added noise showed that utilization of the correlation of determination (R2) as a weighting parameter in ROI evaluation may significantly improve the differentiation between native and transplanted cartilage tissue in noisy images. This could be an added benefit in the non-invasive monitoring of the post-operative status of patients with cartilage transplants if the MR images are not ideal (e.g., lower field strength or lower SNR).

Original languageEnglish (US)
Pages (from-to)2813-2821
Number of pages9
JournalMedical Physics
Issue number6
StatePublished - Jun 2010
Externally publishedYes

Bibliographical note

Funding Information:
Funding for this study was provided by the Vienna Spots of Excellence des Wiener Wissenschafts-und Technologie-Fonds (WWTF)—Vienna Advanced Imaging Center (VIACLIC), the Austrian Science Fund (FWF) FWF-Project No. P-18110-B15, and the Slovak Scientific Grant Agency VEGA No. 2/0142/08.


  • Coefficient of determination
  • Fitting
  • MRI
  • Region-of-interest


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