Locally Sparsified Compressive Sensing for Improved MR Image Quality Fuleah A.Razzaq, Shady Mohamed, Asim Bhatti, Saeid Nahavandi Centre for Intelligent System Research Deakin University Australia Abstract—The fact that medical images have redundant infor- mation is exploited by researchers for faster image acquisition. Sample set or number of measurements were reduced in order to achieve rapid imaging. However, due to inadequate sampling, noise artefacts are inevitable in Compressive Sensing (CS) MRI. CS utilizes the transform sparsity of MR images to regenerate images from under-sampled data. Locally sparsified Compressed Sensing is an extension of simple CS. It localises sparsity con- straints for sub-regions rather than using a global constraint. This paper, presents a framework to use local CS for improving image quality without increasing sampling rate or without making the acquisition process any slower. This was achieved by exploiting local constraints. Localising image into independent sub-regions allows different sampling rates within image. Energy distribution of MR images is not even and most of noise occurs due to under-sampling in high energy regions. By sampling sub-regions based on energy distribution, noise artefacts can be minimized. Experiments were done using the proposed technique. Results were compared with global CS and summarized in this paper. Index Terms—Magnetic Resonance Imaging, Compressive Sensing, Sparse Signals,L1 Minimization. I. I NTRODUCTION The tissues inside the human body have varying sizes and densities, based on location and function of each tissue. Magnetic Resonance Imaging (MRI) is used for analysis, diagnosis and treatment. It is an important imaging technique because it can capture both hard and soft tissues. However, there are some limitations to it. It is a slow and hectic process. Furthermore, the patient required to be motionless during the image acquisition process otherwise a clear and detailed image cannot be achieved. Recent research has been done on Rapid MRI, to acquire good quality images in less time. A faster image acquisition process can save time, effort and delays. Also researchers are interested in rapid MRI because it will allow capturing videos instead of static images. MR image acquisition process is dependent on strength of magnets. A magnetic field is applied to the charge particles inside human body. The energy released by the charged particles form the area under test is recorded using a sensor. Magnets are dependent on their slew rates and other physical properties and hardware cannot be modified for speeding up the image acquisition process. Researchers are working on speeding up MR Image acquisition process by other means, some research has been done using parallel imaging [1]–[5] whereas other work focuses towards reducing the number of samples or measurements that are required for image reconstruction [6]– [12]. Compressive Sensing (CS) works on compressibility of medical images. Medical images are really sparse and can be generated using a small amount of coefficients while discarding other non-significant coefficients. CS-MRI uses this property to reduced required measurements thus resulting in faster image acquisition. However, violation of Nyquist rate can result in noise like artefacts. There is a compromise between speed and quality of image. Lesser measurements means faster acquisition but degraded quality. MR images can have different kinds of noise artefacts; some might be visible and can affect the diagnostic quality of image. These artefacts are critical as they can affect the process of diagnosis and treatment. Noise can be generated due to many reasons e.g. patient movement during scanning, loss of data during signal processing, transmission and due to hardware issues. In CS-MRI under-sampling can result in noise. Inadequate K-space (2-D matrix of Fourier coefficients) data generates wraparound and ringing artefacts. A simple solution is to follow the Nyquist sampling rate which is twice the highest frequency but in that case image acquisition will be slower [13]. This paper defines a framework to use local CS for im- proved image quality. Instead of using one sparsity constraint for whole K-space, local CS uses localised constraints based on multiple sub-regions. The motivation behind this study is the fact that MR images have non-uniform energy distribution. Energy levels vary significantly within image. K-space center is the high energy region and contains most of image energy while away from origin energy levels are relatively low. Under- sampling in high energy region is the reason for most of the image noise. Local sparsity constraints can be exploited for a better image reconstruction. Local CS allows independent sub-regions and different sampling rates within an image. Increasing sampling rate just in high energy regions will result in a better quality image without increasing sampling rate for whole image. On the other hand, low energy areas can be under-sampled further based on energy level in those areas. This paper applies local CS for a faster and a better quality image acquisition. The quality of resultant images was compared to global Compressive Sensing and presented here. 2013 IEEE International Conference on Systems, Man, and Cybernetics 978-1-4799-0652-9/13 $31.00 © 2013 IEEE DOI 2163 2013 IEEE International Conference on Systems, Man, and Cybernetics 978-1-4799-0652-9/13 $31.00 © 2013 IEEE DOI 10.1109/SMC.2013.370 2163