1.3 Thesis organization
1.3.6 Chapter 6
This chapter concludes the research project and highlights the new contributions of this work. It discusses the possible areas of future work for this project and the challenges that were addressed during the implementation of this project for OA. It also mentions the areas in the field of OA diagnosis that have yet to be addressed and the possible challenges and limitation faced by existing methods. It points towards the possible areas that may be undertaken for early stage OA diagnosis and in improving the accuracy and reliability of these methods.
Rician Denoising for Articular
Cartilage in MRI
This chapter is an introduction to Rician noise and its effect on MRI images. Several disadvantages in cartilage detection due to presence of Rician noise have also been iden- tified. In this study we have specifically tried to address better denoising for cartilage, using an adaptive filter with edge preservation for MRI images affected by Rician noise. Also as Rician noise is nonlinear and signal dependent, we have conducted another study to address this dependence of noise on signal, while the third study implements a non-linear signal dependent filter to address Rician noise.
The results of this study have been published in the following
Aarya I., Jiang D., and Gale T., “Adaptive Rician Denoising with Edge Preserva- tion for MR Images of the Articular Cartilage”. J. Computer Methods in Biome- chanics and Biomedical Engineering: Imaging & Visualization. 2014, pp 1-10 (Aarya et al.,2014)
Aarya. I, Jiang D. and Gale T., “Adaptive SNR Filtering Technique for Ri- cian Noise Denoising in MRI”. Biomedical Engineering International Conference (BMEiCON), 2013 6th IEEE conference, pg. 1- 5 (Aarya et al.,2013)
Aarya I., Jiang D. and Gale T., “Signal Dependent Rician Noise Denoising using Nonlinear Filter”. Lecture Notes on Software Engineering, 2013, 1(4) 344-349 (Aarya et al.,2013)
2.1
Rician noise and MRI
Osteoarthritis is a chronic joint disease affecting a large percentage of the world’s popu- lation (Eckstein et al.,2006). It is mainly characterized by degradation of the cartilage tissue, with loss in volume of the cartilage as the disease progresses (Eckstein et al., 2006). Articular cartilage in healthy patients is 1.3 - 2.5 mm thick and less in patients suffering from Osteoarthritis (Eckstein et al.,2006). Due to its superior soft tissue con- trast, MRI offers better visualization of the cartilage which enables to identify changes in the cartilage thickness and morphology (Adams and Wallace, 1991; Eckstein et al., 2006). These changes in the cartilage tissue may be used to predict various stages of disease progression in Osteoarthritis. MRI can therefore provide a non-invasive method for diagnosis of Osteoarthritis and help quantify the articular cartilage data (Kumar et al., 2011; Ding et al., 2007). To help in diagnosis one should be able to correctly identify the cartilage tissue and accurately isolate it from its surrounding joint structure for a quantitative analysis (Eckstein et al.,2006;Ding et al.,2007). A common problem faced for cartilage study, is the similarity in tissue contrast of the cartilage with the sur- rounding joint tissues (Cashman et al.,2002). This task is made even more difficult due to the reduced contrast ratio of the image in presence of noise. This reduced contrast ratio makes it difficult to differentiate between cartilage boundaries and the surrounding fluid, causing error in diagnosis (Cashman et al.,2002). Hence it is essential to reduce the effect of noise and improve image contrast to properly identify the cartilage tissue within the joint structure without any loss of cartilage information.
Noise is introduced in the MRI image due to limitations in the data acquisition time (Rajan et al., 2012). This noise in the k-space data is considered to be uncorrelated zero-mean Gaussian (Rajan et al.,2012). A magnitude image is obtained by computing the magnitude of the real and imaginary k-space data (Nowak,1999;Gudbjartsson and Patz, 2005). MRI images are converted to magnitude images to avoid phase artefacts (Gudbjartsson and Patz,2005). Due to this nonlinear operation noise follows a Rician distribution and is known as Rician noise. This noise is nonlinear and signal dependent and may significantly affect the image quality and contrast thus making it difficult to perform cartilage diagnosis (Adams and Wallace, 1991; Rajan et al.,2012). For single coil MRI data, the noise affects SNR and the overall contrast of the image (Sijbers et al., 1998). Rician noise displays a varying distribution depending on the SNR of the image (Sijbers et al.,1998;Nowak,1999). Images exhibiting low SNR tend to follow a Rayleigh distribution while those with a higher SNR approximately follow a Gaussian distribution (Nowak,1999). The magnitude image equation for MRI is given by Eq. (2.1) and its Rice
Figure 2.1: Rician probability distribution function for different standard deviations of noise and intensitiesGudbjartsson and Patz,2005
distribution function is given by Eq. (2.2) (Nowak,1999;Gudbjartsson and Patz,2005).
M = q (A+nr)2+n2i (2.1) P(M|A, σn) = M σ2 n exp(−M 2+A2 2σ2 n ) I0( A M σ2 n ) (2.2)
Where M represents the observed pixel intensity affected by noise, A represents true signal intensity, nr represents real component of noise and ni represents the imaginary
component of noise. P is the Rician distribution function of noise in magnitude image and requires prior information of true signal intensity A. The variance of noise is given by σn andI0 is the zero-order modified Bessel function (Gudbjartsson and Patz,2005).
As noise affects the original pixel intensity, it is essential that the denoising procedure helps to restore this original image information. This might be a difficult task, as the original nature of the signal is unknown to the user and actual variance of noise is seldom known. Adequate denoising can be achieved if one can correctly determine the value of variance of noise and its distribution within the image. This information about the noise may then be used to restore the image.
In the background of the MRI image where intensity of the signal function is zero, Rician noise follows a Rayleigh distribution (Gudbjartsson and Patz,2005). This characteristic feature of Rician noise is often used to estimate the variance of noise in the image. The probability distribution function of Rayleigh noise is given by Eq. (2.3) and its mean is given by Eq. (2.4) (Gudbjartsson and Patz,2005).
P(M) = M σ2exp( −M2 2σ2) (2.3) ¯ M =σ r π 2 (2.4)
The noise in the magnitude MRI image can thus be obtained from the background of the image, where the signal function intensity is zero (Tran and Jiang, 2012). This estimation of noise is also used to carry out the denoising process. For higher SNR regions the Rician distribution function can be given by Eq. (2.5) and is very similar to the Gaussian distribution function (Gudbjartsson and Patz,2005).
P(M)≈ √ 1 2πσ2exp
−(M−√A2+σ2)2
2σ2 (2.5)
The observed mean for the above distribution is very close to the actual mean of the signal function but may contain some bias due to the presence of noise (Gudbjartsson and Patz, 2005; Tran and Jiang, 2012). The bias can be corrected by using Eq. (2.6) (Gudbjartsson and Patz,2005).
˜
A=p|M2−σ2| (2.6)
While noise may be Rician for single coil systems it may no longer be Rician for multi- coil systems (Rajan et al., 2012). In MR images acquired with the parallel imaging techniques using multiple coil system, noise is highly inhomogeneous. Assuming that the noise components are still independent and identically distributed (IID); the envelope of the magnitude signalML(x) will follow a non-central chi distribution with probability
distribution function PML(ML|AL, σn, L) = A1L−L σ2 n MLLe −ML2+A2L 2σn2 I L−1( ALML σ2 n )µ(ML) (2.7)
WhereLis the number of coils and reduces toL= 1 for single coil systems. In the back- ground this probability distribution function (PDF) reduces to central chi-distribution with PDF as (Rajan et al.,2012),
PML(ML|σn, L) = 21−L Γ(L) ML2L−1 σ2L n e −ML2 2σn2 µ(ML) (2.8)
above equation will become Rayleigh when L = 1. In such systems noise is still non- linear function but with a chi-square distribution function.