MRI Signal Processing and Imaging - Report Example

MRI SIGNAL PROCESSING AND IMAGING By Student’s name Course code and name Professor’s name University name City, State Date of submission Abstract MRI poses several advantages to the medical imaging fraternity. The images obtained have however been found to contain a lot of discrepancies that need to be addressed prior to analysis by medical practitioners. It is therefore the mandate of this project to establish the most suitable method among the existing ones to reconstruct images that amount from the MRI exercises. The major objectives of study are identified as a need to familiarize with the tools utilised for MRI image reconstruction through a practical approach, addressing the methodologies applied in MRI image reconstruction, establishing the differences between the existing methods of image reconstruction through a practical approach and recommending on suitable parameters of achieving high quality MRI images as a learning outcome. The limitations however are indicate as the inability to work eith Matlab at the beginning of this study but this weakness is eventually overcome during the project execution period. As an approach towards learning the possible outcomes of Matlab, the PULSAR open source toolbox is studied to offer a foundational approach towards the completion of this project. It is established that k-space data simulation is highly applicable in GRAPPA image reconstruction methodology while SENSE methodology uses the aliasing images approach as the principle towards image reconstruction. A dispute does not however arise on the mode of arriving at the final image since these methodologies offer a high quality outcome as is evident from the reconstruction experiments staged. The incorporation of these methodologies within the MRI equipment console is called for so as to offer an optional approach towards image improvement. This is also owed to the fact that these methodologies are conducive for deployment in different body parts. Acknowledgement I would like to thank the almighty for giving me a spirit of hard work and wisdom to complete this research. I would especially like to thank my supervisor ________ who has guided me relentlessly in completing this project. Besides that, it is my sincere appreciation to my immediate family and friends for the support and encouragement that they extended me during the period I was working on this report. Finally, I wish to thank the Faculty of Engineering and Industrial Sciences and all those who contributed to the success of this project in one way or the other. Declaration I hereby declare that except where reference has clearly been made to work by others, all the work presented in this report is my own work; that it has not previously been submitted for assessment; and that I have not knowingly allowed any of it to be copied by another student. I understand that deceiving or attempting to deceive examiners by passing off the work of another as my own is plagiarism. I also understand that plagiarising the work of another or knowingly allowing another student to plagiarise from my work is against the University regulations and that doing so will result in loss of marks and possible disciplinary proceedings against me. Signed ………………………………………… Date ………………………………………… Table of Contents Abstract 2 Acknowledgement 3 Declaration 4 List of Illustrations 6 1.0 Introduction 7 1.1Overview of MRI Technique 8 1.2Research Rational 10 1.3Research Objectives 10 1.4Limitations of Study 11 2.0 MRI Image Reconstruction 12 2.1 Matlab Simulation tool 12 2.2 Simulation of Coil Sensitivity 14 2.3 k-space Data Simulation 15 2.4 GRAPPA Image Reconstruction Technique 16 2.4.1 Results of GRAPPA Image Reconstruction 18 2.5 SENSE Image Reconstruction Technique 20 2.5.1 SENSE Reconstruction Results 22 3.0 Conclusion 25 4.0 References 27 Appendix 1: Matlab Reconstruction Code for GRAPPA Method 28 Appendix 2: Matlab Reconstruction Code for SENSE Method 30 List of Illustrations Figure 1: Schematic representation of magnetic resonance imaging (MRI) (Universe Review, 2011). 9 Figure 2: Layout of Matlab PULSAR toolbox (Ji, et al., 2007). 14 Figure 3: Eight channel head array. 19 Figure 4: A two image array showing reference image and reconstructed image using GRAPPA methodology. 20 Figure 5: g-factor map to be used in obtaining a reconstructed image using SENSE. 24 Figure 6: A summation of all aliased images to achieve a reconstructed image using SENSE methodology. 25 1.0 Introduction Achievements made in medical imaging have seen the introduction of various useful methodologies in the 20th century. Apart from the common technologies such as X-ray imaging and visual imaging which have been extensively deployed magnetic resonance imaging (MRI) has emerged as an advantageous approach. The basic radiofrequency of MRI operation ranges from 10 to 200MHz of the electromagnetic spectrum (Bushong, 2003). Some of the advantages that are widely quoted for the use of MRI have a propensity towards the safety of a patient owing to the mode and quality of imaging. Images associated with MRI possess a superior contrast in comparison radiography making it easier to differentiate among low contrast tissues. Images produced by MRI are also considered to be superior in terms of the spatial resolution (ability to identify a small object). Unlike other methods of imaging such as X-ray, MRI has been found to give better results in multiplanar imaging based on the ability to achieve direct transverse, coronal, oblique plane and sagittal images. Magnetic resonance spectroscopy has highly contributed to the possibility of precise identification between tissues for purposes of analysis. Lastly, MRI does not produce ionization radiations since it uses RF electromagnetic radiations and associated magnetic fields. Ionization radiations have been found to be responsible for long term side effects on the patients whose images are taken using methodologies such as X-ray. 1.1 Overview of MRI Technique The magnetic resonance imaging hardware consists of three major components namely; a magnet, computer and an operating console. The magnet comes in form of a huge cylinder that is capable of accommodating a grownup patient during the imaging process. A computer that is provided together with an MRI kit is fast and capable of carrying out multiple commands at any given instance due to the amount of data that emanates from this imaging technique. The MRI console comes in a standard form that offers annotations and post-processing information that is well known to operators if the technologies that predecessor technologies apply. The only difference however is that the MRI console is availed with the gradient magnetic fields and RF pulses control (Bushong, 2003). Figure 1: Schematic representation of magnetic resonance imaging (MRI) (Universe Review, 2011). Bloch and Purcell based MRI imaging on the positively charged spinning nucleus of hydrogen due to the presence of water in human tissue. When the hydrogen atoms spin, they form a minute magnetic field which is compared to that of a compass needle. Introducing a magnetic field is prone to polarise the hydrogen atoms thereby aligning them between two directions. Introducing a radiofrequency energy at the Larmor resonance phase forces protons aligned with the magnetic field to reverse their direction subsequently absorbing a lot of energy. Energy release times labelled as T1 and T2 depend on the chemical and physical properties of the tissues that are under study at any given time. This relaxation causes production of magnetic resonance signal which is tapped by local coils which are used to optimise image quality (Edelman & Warach, 1993). Magnetic resonance images are represented by localised signal intensities. This depends on the strength of the magnetic field involved in the production of images also known as pulse sequence. Further to this, it is clear that relaxation times T1 and T2 mentioned above are responsible for the image quality. Other physical parameters that are involved in the determination of image quality include the density of mobile protons, magnetic susceptibility of tissues, physical and chemical composition and lastly the nature of blood flow in a given area of the body (Edelman & Warach, 1993). Pulse sequence is very important when it comes to the weighting exercise since it determines the repetition and echo time as shall be observed in the practical section of this project. 1.2 Research Rational This project is mainly motivated by the urge to understand and resolve the major issues that face the improvement of images prior to analysis by medical practitioners. It has emerged that despite the advantages that MRI poses towards the medicine field there are improvements that should be made to achieve better quality images faster. The loud noises that emerge from the MRI images is at times misleading and should be eliminated through the existing or new applicable forms of image reconstruction. This research however focuses on two main image reconstruction algorithms namely; GRAPPA and SENSE for implementation within MRI. GRAPPA is a denotation of the phrase Generalized Autocalibrating Partially Parallel Acquisitions founded which is basically utilised to reconstruct the k-space data that is deemed to be missing (Wang, et al., 2011). These combinations may be either linear on nonlinear depending on how the data acquired is combined to eliminate the pending errors. This study is also motivated by the use of SENSE for image reconstruction in order to offer a comparative approach. This algorithm offers image correction by enhancing the acceleration factor for phase encoding purposes. The general user interface provides a reconstruction of parameters that are parallel as well as analysis of quality of the final image (Omer & Dickinson, 2010). 1.3 Research Objectives The main objectives of this study are to: i. Familiarize with the tools utilised for MRI image reconstruction through a practical approach. ii. Study the methodologies applied in reconstruction of images emanating from MRI. iii. Establish differences between the existing methods of image reconstruction through a practical approach. iv. Recommend on suitable parameters of achieving quality MRI images. 1.4 Limitations of Study This study is limited by basic limitations such as the ability to learn the methods of image reconstruction ahead of schedule. Apart from learning about the image reconstruction approaches, it is mandatory to familiarise with at least one tool through which to implement the GRAPPA and SENSE methodologies. As a matter of fact Matlab was chosen as the tool in which to deploy the methodologies above due to its simplicity nature of coding. 2.0 MRI Image Reconstruction As indicated in the introductory section above, the main objectives of this study are to learn on how to apply the tools deployed for MRI image reconstruction in order to give conclusive remarks on the issue of image quality improvement. This section therefore covers data acquisition, the technologies that are deployed in image reconstruction, the Matlab simulation exercise and the expected outcome. Images obtained from the simulation exercise are also exhibited in accordance to the technology applied for review and comparison. 2.1 Matlab Simulation tool Matlab is identified as a very important tool in this research due to the simulation capabilities that it poses towards MRI experiments. This is a cross platform tool which poses many advantages to learners in that it is programmed in a language that is easy to understand. To add to this, there are several default commands that have been written and availed publicly for illustration purposes in case of beginners. Plugins discovered by the likes of Ji et al. (2006) and Guerquin-Kern (2012) come in as handy solutions when it comes to handling of the complex functions associated with GRAPPA and SENSE MRI image improvement techniques. The technique that shall be deployed in this study shall mainly exploit the noise removal tool in order to improve the quality of images that shall be achieved. The images obtained from both approaches i.e. GRAPPA and SENSE shall then be compared with the initial images to gauge the improvements that have been made. It should however be noted from the onset of this experiment that the corrected images shall not be perfect as promised. The provided demonstration scripts for Matlab include DemoSimuAndRecon.m which is aimed at defining the parallel setting of the MRI experiment. This is dependent on the favourable settings that result from the image obtained from the exercise. Secondly, the DemoBrainEPI.m script is provided for purpose of echo planar image improvement when it comes to the k-space on the Cartesian plane. This script is applied for coil sensitivity and the resulting dataset usually suffers from lack of homogeneity in the static field. Lastly, the DemoBrainSpiral.m script that is provided together with Matlab is used for computing the receiving coil sensitivity maps. Executing this code in Matlab subject to a given image results to data modulation which leaves the upper left corner of the image with tremendous improvements (Guerquin-Kern, 2012). For parallel magnetic resonance to be successful the formation data engages the model in equation 1 below. (1) Where represents the receiving coil sensitivity map. represents the k-space position. is the signal to be imaged. Based on the above equation, the data simulation model shall take the form of a k-space data (and any other data that may be required to make the reconstruction exercise successful. MATLAB has developed an open source tool called Parallel imaging Utilizing Localized Surface-coil Acquisition and Reconstruction (PULSAR) as a research platform for parallel MRI. This study shall hence benefit from its three modules namely; k-space data and coil sensitivity simulation, partial parallel imaging (PPI) methodology and the artefact power (AP) performance evaluation. The advantages of this structure is that it can synthesise multichannel data for any given type of coil geometry and raw data read into the image function for rectification (Ji, et al., 2007). Figure 2: Layout of Matlab PULSAR toolbox (Ji, et al., 2007). 2.2 Simulation of Coil Sensitivity Applying the PULSAR technology for simulation of coil sensitivity requires enactment of rectangular loops. This assumption is quasi-static and the wavelength at the Larmor frequency is therefore larger than that of the object to be imaged. In this case, the Matlab code incorporated within PULSAR tool box ensures that the Biot-Savart law shown in the equation (2) below is included. (2) Where represents the vector of a point from the wire to the image grid is the current being carried by the wire is differential path along the wire. And is the unit vector. B is concerned with a three dimensional coverage of the MRI based on transverse nature of magnetization which subsequently produces significant signal worth review for image reconstruction. This is presented in form of a linear matrix. Since it is assumed that the coil loops are placed in a field parallel to then the effective coil sensitivity function implemented by Matlab PULSAR is (Ji, et al., 2007). 2.3 k-space Data Simulation It has been established in the PULSAR program that simulation of a given test image depends on the field of view (FOV), coil sensitivity and voxel size. In order to produces fully encoded k-space data, the coil sensitivity function and that of the image are multiplied then a discrete Fourier transform applied. Further to this, acquired data is imposed to complex Gaussian noise together with the zero mean, and circular symmetry depending on the data points achieved during the calculations. Variances contained in noise however are as a result of real and imaginary noise. Based on this statement, it is easy to establish the relationship between these two parameters as. The Fourier transform for MRI reconstruction normally covers an orthogonal exercise, the average signal-to-noise ratio (SNR) achieved usually equals to each of the image’s SNR pixels. This equation can therefore be represented as shown in (3) below; (3) Where is the square signal intensity, is the signal-to-noise ratio in decibels And represents the noise factor arising from encountered complexities. In order to trigger under-sampled datasets, it is advisable to decimate data from all channels depending on the imaging methodology to be applied and the expected reduction factors. Matlab offers an approach of getting the phase encoding lines which are centred to indicate uniform under-sampling. 2.4 GRAPPA Image Reconstruction Technique GRAPPA linearly combines the k-spaces which are deemed as under-sampled for the purpose of auto-calibrating the missing signals. During reconstruction process, the images suffer from high noise levels and aliasing artifacts. Linear combination of acquired data is therefore necessary to ensure that the combination coefficients achieved achieve the estimated auto-calibration signal within the central k-space. Apart from the linear methods that have been developed to improve GRAPPA reconstruction, there exist other methods such as GRAPPA using localised coil calibration. The errors that are observed in this kind of setup are related to truncation and inversion due to extension of model errors and noise. The model error originates from the auto-calibration signal (ACS) lines and data truncation in order to generate noise-induced estimation errors. Least squares of iterative nature are therefore utilised to ensure that this kind of noise is reduced to the lowest possible coefficients. This approach is however impossible due to computational complexities that have been observed over time (Wang, et al., 2011). Localised coil calibration is therefore suggested as the preliminary approach for cross-sampling in order to achieve improved linear GRAPPA. This method shall employ the acquisition of ACS lines along the orthogonal of the under-sampled lines. This shall ensure that the ACS data achieved in this direction is significantly deployed in image quality improvement. According to Wang, et al. (2011), the improvements carried out on the k-space shall depend on the chemical shift and eddy currents that occur in different directions. The experiment aims at reducing the artifacts resulting from GRAPPA reconstruction in accordance to the same number of ACS lines. This move is aimed at considerably increasing the speed of scanning through an increased image SNR. Assuming that the k-space lines achieved for this experiment are uniformly spaced, ACS lines to be acquired in execution of the Matlab coding shall utilise the under-sampled lines. This is to ensure that each line gives correspondence to phase encoding as an approach for time reduction which is one of the paramount goals to be achieved in this study. Reconstruction of k-space data missing shall therefore utilise the linear equation (4) below for conventional GRAPPA. (4) Where is the offset from the obtained line, is the outer reduction factor (ORF), is the column from the offset to be reconstructed, and are the neighbouring block indices, and are the neighbouring columns indices. Combining the index counts through the individual coils for block indices and is meant to reconstruct given areas through 4 blocks and 3 columns approach also referred to as kernel. This is an iterative process that ensures that each of the locations projected by each coil is covered resulting to L single coil images that are not combined in any way. This is approached using Fourier transform on the un-combined coils to carry out a sum-of-squares (SoS) reconstruction (Wang, et al., 2011). For experimental approach, this formula together with the Fourier transform have been deployed in order to better the images as shown in figure 3 and 4 below. 2.4.1 Results of GRAPPA Image Reconstruction The results obtained indicate that the SNR ratio is high in comparison to the artifact power. The coil sensitivities are also not localised as compared to the initial image due to banding and high contributory factors due to under-sampling. GRAPPA is therefore found to work better under spatial harmonics when it comes to linear arrays for the purpose of reconstructing images obtained from the head. It can also be concluded that GRAPPA is paramount when it comes to sensitivity estimation for self-calibrated data. The images obtained for the MRI eight channel array reconstruction using GRAPPA are shown in the figure below. Figure 3: Eight channel head array. Despite the computational complexities that is encountered in the GRAPPA methodology of MRI image reconstruction, the experimental setup manages to obtain images based on diligence. The applied set of parameters is contained in appendix 1 of the coding used to come up with the GRAPPA reconstruction imaging. The images below portray the differences between the initial image and the final image that is due for analysis by the medical practitioners. Figure 4: A two image array showing reference image and reconstructed image using GRAPPA methodology. 2.5 SENSE Image Reconstruction Technique Parallel acquisition of MRI images is also applied in SENSE image reconstruction technique. A generalised algorithm has been deployed by Omer & Dickinson (2010) in their approach through utilising an acceleration index of 2 to 8 coupled with phase encoding to achieve very good results. This features motivate this study in that SENSE algorithm also aims at coming up with improvements for timely implementation of the achieved MRI images for cost reduction. This is one of the problems that the objectives enlisted in the introductory section which to uncover. In this method, multiple coils are utilised in order to acquire the right data for analysis within the reconstruction tool (Matlab). This method also combines the two common algorithms namely k-space and image-domain. The receiver sensitivity of the SENSE methodology of reconstruction contains an encoding that complements Fourier linear gradients. This however do not project into the area being imaged by the MRI for signal collection but move further from the coil. The systematic nature in which the coils are arranged within the implementation location captures spatial information of the object that is pending reconstruction. Parallel imaging ensures that the image acquired possesses k-space lines with an increased gap. This acts as a challenge towards the analysis and reconstruction of images thus they are omitted to reduce the time involved in the acquisition of the MRI images. The sampling process for k-space leaves a lot to be desired due to aliasing that occurs among the acquired images thus the need to reconstruct them. The actual image location contributes towards the pixel locations for the subsequent images which calls for signal contribution to allocate right pixels through a reconstruction process. Good reconstruction through deployment of SENSE is achieved when the coils’ sensitivity profile differs from that of the different locations that appear in the signal components. Therefore when it comes to quality of the resulting image, SENSE reconstruction highly depends on the sensitivity map’s accuracy. The weighting process is usually deployed for the purpose of differentiating the signals from the aliased images with those of the respective locations. Signal superposition is carried out using different coil snesitivities in accordance to the achieved weights. The significance of this fact is that the attention of many researchers is usually drawn to the regulation techniques for proper estimation. It is therefore paramount to have a precise sensitivity map if SENSE technique is intended to carry out corrective measures on images obtained by MRI (Omer & Dickinson, 2010). SENSE methodology applies the wide knowledge about coil element sensitivities in order to come up with calculations that are meant to establish the aliased signal component for each point. Considering that the gap is increased by an acceleration factor then the signals within these locations shall have to be spaced equally prior to making any assumptions. Calculating the field of view reduction results folds an aliased representation with a total number of signals present. This is due to the aliasing of the actual signal location which is achieved through displaced iteration as well as superposition by applying the expression (5) below. (5) Where is the number of coil array elements. represents the number of overlapped signal. represents the encoding sensitivity matrix. is the aliased magnetization value. 2.5.1 SENSE Reconstruction Results Due to skipping of phase encoding lines the results is tremendous when it comes to the SNR ratio. Therefore, the trajectories utilized in image reconstruction have different designs in order to cater for these losses. Each RF coil is allocated its own spatial information causing low image quality. Due to high acceleration factors and usage of several receivers, the image matrix becomes poorly reconditioned leading to noise amplification. Examining image reconstruction, it is noted that a single element array is generally confine to a certain given location whose noise values become distributed across the whole image. Other sources of noise are weakly correlated resulting to image growth as the number of signals continue to be aligned with equally sensitive coils. The data that is achieved due to the acceleration factor is used to reconstruct the final image. Noise amplification is further reused to come up with natural correlation so that some of the points with lower amplifications can be at par with the related points. Noise quantification is carried out by the g-factor which also offers a descriptive approach to array encoding. As shown in the figure below achieved in the experiment, the magnetization distribution is indicated by the colour intensity. A smaller g-factor translates to the fact that the magnetization was carried out by several coil elements. Greater sensitivity can however be recovered when the array can detect the magnetization in a given element. Figure 5: g-factor map to be used in obtaining a reconstructed image using SENSE. Applying the reconstruction algorithm presented in Appendix 2, the sum of the square is done effectively to achieve a high quality reconstructed image. Applying the Fourier transform while carrying out the reconstruction operation produces the image whose k-space data was truncated according to the FOV required. The noise images obtained while carrying out the switching of RF signals are imposed against arrays whose sensitivity is high on the x and y axis creating inconsistencies. These results were bettered through regularization of coil design in a corresponding ration to the factors of acceleration as an improvement approach towards the SNR. This reduced the artifact power thus resulting to the corrected image shown in the figure below alongside its aliased images. Figure 6: A summation of all aliased images to achieve a reconstructed image using SENSE methodology. 3.0 Conclusion Using a detailed approach in coming up with reconstructed images for MRI is paramount to the betterment of services within the medical field. The objectives of this study are achieved in that the images achieved in the long run indicate a better quality. Enacting the SENSE and GRAPPA algorithms separately within the user interface of the MRI equipment is necessary due to the contributions that each image analysis methodology poses to the medical fraternity. The results obtained in SENSE in particular are enhanced by the g-factor map which causes loss in SNR. GRAPPA method on the other side is keen to suppress residual aliases through reduction of ACS lines. 4.0 References Bushong, . S. C., 2003. Magnetic Resonance Imaging, Missouri: Elsevier Health Sciences. Chang, Y., Liang, D. & Ying, L., 2011. A kernel approach to parallel MRI reconstruction. National Science Foundation, pp. 1-4. Edelman, R. R. & Warach, S., 1993. Magnetic Resonance Imaging. The New England Journal of Medicine, Volume 1, pp. 708-716. Guerquin-Kern, M., 2012. Matlab Code for MRI Simulation and Reconstruction, s.l.: École polytechnique fédérale de Lausanne. Ji, J. X., Son, J. B. & Rane, S. D., 2007. PULSAR: A MATLAB Toolbox for Parallel Magnetic Resonance Imaging Using Array Coils and Multiple Channel Receivers. Concepts in Magnetic Resonance Part B (Magnetic Resonance Engineering), 31B(1), pp. 24-36. Omer, H. & Dickinson, R., 2010. A Graphical Generalized Implementation of SENSE Reconstruction Using Matlab. Concepts in Magnetic Resonance Part A, 36A(3), pp. 178-186. Universe Review, 2011. Tomography (CAT, PET, MRI). [Online] Available at: http://universe-review.ca/I10-63-MRI.jpg [Accessed 4 June 2014]. Wang, H. et al., 2011. Cross-Sampled GRAPPA for Parallel MRI. National Science Foundation, pp. 1-4. Wang, H. et al., 2011. Cross-Sampled GRAPPA for Parallel MRI. National Science Foundation, pp. 1-4. Appendix 1: Matlab Reconstruction Code for GRAPPA Method %%%%%% GRAPPA Method for Parallel MRI Reconstruction" %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% warning off all coil_num=8; rfac=5;%outer reduction factor temp = zeros([256,256,coil_num]);% create an empty matrix to contain the image data ( 256x 256x8) load data_brain % read the data from the data file for k = 1:coil_num temp(:,:,k) = fftshift(ifft2(fftshift(full_kspace_data(:,:,k))));% actually the data was saved into an array name "full_kspace_data" end %getting the reference image c=0; for k=1:coil_num a=real(temp(:,:,k)); b=imag(temp(:,:,k)); c=a.*a+b.*b+c; end Ref_image=sqrt(c); amp=abs(Ref_image); amp_ref=amp; figure;imshow(Ref_image,[0 max(amp_ref(:))*0.5]);% show the reference image Img_NMSE=Ref_image/mean(mean(abs(Ref_image))); [d1,d2,d3]=size(temp); ndim=d1;%phase encoding direction off = 0;%starting sampling location % The number of ACS lines nencode=24;%%% when you change the number of ACS lines, you can change the reconstructing time also. % The convlution size num_block=2; num_column=15; % Obtain ACS data and undersampled data acs_line_loc=(ndim/2+1-nencode/2):(ndim/2+nencode/2); for l=1:coil_num k_space_full=fftshift(fft2(temp(:,:,l))); k_space_red(:,:,l)=k_space_full((off+1):rfac:(d1-off),:); acs_data(:,:,l)=k_space_full(acs_line_loc,:); end % Obtain uniformly undersampled locations pe_loc=(off+1):rfac:(d1-off); % Net reduction factor acq_idx = zeros(d1,1); acq_idx(pe_loc) = 1; acq_idx(acs_line_loc) = 1; NetR = d1 / sum(acq_idx); % GRAPPA Reconstruction times_comp = 3;%The number of times of the first-order terms % show the image reconstructing time%%%%%%%%%%%%%%%%%%%%%%%%%%5 tic [full_fourier_data1, ImgRecon1, coef1] = grappa_function(k_space_red, rfac, pe_loc, acs_data, acs_line_loc, num_block, num_column, times_comp); toc %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure, imshow(abs(fftshift(ImgRecon1)),[0 max(amp_ref(:)*0.5)]);% reconstructed image Appendix 2: Matlab Reconstruction Code for SENSE Method clear all clc close all %Step1, simulating the subsampled data and coil-calibration data load data_brain.mat;%loading brain data % Inilitalization FOV_full = 1; FOV_subsampled = 1/4; FOV_reduction_factor = round(FOV_full/FOV_subsampled); Rnoise = eye(8); %noise correlation matrix betweent channels % k-space data sumsampling [reduced_kspace_data, Subsampling_locations] = sample_kd(full_kspace_data,FOV_reduction_factor); save('subsampled_kdata','reduced_kspace_data', 'Subsampling_locations','FOV_reduction_factor','Rnoise'); % coil sensitivity calibration data from the central k-space Num_centrallines = 32; [Nfe,trash,Ncoil] = size(reduced_kspace_data); for ch=1:Ncoil central_kdata(:,:,ch) = datacrop2d(full_kspace_data(:,:,ch),Nfe,Num_centrallines); end save('8ch_centralkdata','central_kdata'); clear %Reconstruction processing load('subsampled_kdata'); %sensitivity estimation Npe_tobe = size(reduced_kspace_data,2)*FOV_reduction_factor; % sensitivity estimate filename='8ch_centralkdata.mat'; datatype =2; % Different types of filters to choose: %If you want to choose any filter,just uncomment the command line for that filter %and comment the command lines for the rest of filters. % This gives you a better comparsion of the reconstructed images used by different filters. % Filters.type ='polynomial'; Filters.Poly_Order = 1; Filters.poly_Wc=5; Filters.poly_Wr=5; %for polynomial filtering Filters.type ='hamming'; % Hamming filter %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %----------------------------------------------------------------------------------------------------- [channelsensitivity, ROI_mask]= sensitivity_estimation(filename, datatype, Npe_tobe,Filters,Rnoise); %sense reconstruction [recon_sense, flag,gmap] = sense(channelsensitivity, reduced_kspace_data, FOV_reduction_factor); %error map %sum of square(sos) reconconstructed image as "standard" load data_brain.mat; sos = recon_sumofsquares(full_kspace_data,0, Rnoise); error_image = abs(abs(recon_sense) - sos); L2diff=norm(error_image(:)) % Show the results figure(1); imagesc(abs(recon_sense)); colormap('gray'); axis square; colorbar;title('sense reconstructed image'); figure(2); imagesc(abs(sos)); colormap('gray'); axis square; colorbar;title('sum of squares reconstructed image'); figure(3); imagesc(error_image); colormap('gray'); axis square; colorbar; title(sprintf('reconstructed image error: %s',L2diff)); figure(4); imagesc(gmap); colorbar; axis square; title('g-factor map'); Read More

Magnetic resonance images are represented by localised signal intensities. This depends on the strength of the magnetic field involved in the production of images also known as pulse sequence. Further to this, it is clear that relaxation times T1 and T2 mentioned above are responsible for the image quality. Other physical parameters that are involved in the determination of image quality include the density of mobile protons, magnetic susceptibility of tissues, physical and chemical composition and lastly the nature of blood flow in a given area of the body (Edelman & Warach, 1993).

Pulse sequence is very important when it comes to the weighting exercise since it determines the repetition and echo time as shall be observed in the practical section of this project. 1.2 Research Rational This project is mainly motivated by the urge to understand and resolve the major issues that face the improvement of images prior to analysis by medical practitioners. It has emerged that despite the advantages that MRI poses towards the medicine field there are improvements that should be made to achieve better quality images faster.

The loud noises that emerge from the MRI images is at times misleading and should be eliminated through the existing or new applicable forms of image reconstruction. This research however focuses on two main image reconstruction algorithms namely; GRAPPA and SENSE for implementation within MRI. GRAPPA is a denotation of the phrase Generalized Autocalibrating Partially Parallel Acquisitions founded which is basically utilised to reconstruct the k-space data that is deemed to be missing (Wang, et al., 2011). These combinations may be either linear on nonlinear depending on how the data acquired is combined to eliminate the pending errors.

This study is also motivated by the use of SENSE for image reconstruction in order to offer a comparative approach. This algorithm offers image correction by enhancing the acceleration factor for phase encoding purposes. The general user interface provides a reconstruction of parameters that are parallel as well as analysis of quality of the final image (Omer & Dickinson, 2010). 1.3 Research Objectives The main objectives of this study are to: i. Familiarize with the tools utilised for MRI image reconstruction through a practical approach. ii. Study the methodologies applied in reconstruction of images emanating from MRI. iii. Establish differences between the existing methods of image reconstruction through a practical approach. iv. Recommend on suitable parameters of achieving quality MRI images. 1.4 Limitations of Study This study is limited by basic limitations such as the ability to learn the methods of image reconstruction ahead of schedule.

Apart from learning about the image reconstruction approaches, it is mandatory to familiarise with at least one tool through which to implement the GRAPPA and SENSE methodologies. As a matter of fact Matlab was chosen as the tool in which to deploy the methodologies above due to its simplicity nature of coding. 2.0 MRI Image Reconstruction As indicated in the introductory section above, the main objectives of this study are to learn on how to apply the tools deployed for MRI image reconstruction in order to give conclusive remarks on the issue of image quality improvement.

This section therefore covers data acquisition, the technologies that are deployed in image reconstruction, the Matlab simulation exercise and the expected outcome. Images obtained from the simulation exercise are also exhibited in accordance to the technology applied for review and comparison. 2.1 Matlab Simulation tool Matlab is identified as a very important tool in this research due to the simulation capabilities that it poses towards MRI experiments. This is a cross platform tool which poses many advantages to learners in that it is programmed in a language that is easy to understand.

To add to this, there are several default commands that have been written and availed publicly for illustration purposes in case of beginners.

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