te ir hnol

Compressive sampling MRI sam nd ta. erim tio et raw ltiucti sampling method. The proposed sampling method is signal dependent and the estimation of sampling locations is robust to noise. As a result, it eliminates the necessity of mathematical model and parameter sampling patterns as required in non-adaptive sampling methods. © 2015 Elsevier Inc. All rights reserved. truction fewer challe amplin to CS n und partic k-space adaptively, tral profile extracted ta) [13]. This method eliminates the necessity of a mathematical model and a parameter tuning (for sampling pattern computation) as the probability density

Magnetic Resonance Imaging xxx (2015) xxx–xxx

Contents lists available at ScienceDirect

Magnetic Res n wwof k-space to be undersampled. Because of its non-adaptive strategy (signal independent), it is considered as a robust sampling methodperforming transform point spread function analysis (to get best incoherence) [7–9]. Sampling patterns are generated based on a polynomial function which is tuned to match the energy distribution to impose a prior knowledge. To sample a sampling patterns are computed from a spec from already acquired data (similar k-space dasamples are acquired at the center of k-space and the sampling density is decreased gradually as the trajectory moves towards periphery of k-space. This variable density sampling method is extended to CS MRI to get an optimum sampling pattern by used to speed up the acquisition and to improve the reconstruction accuracy [12]. Using a prior knowledge about the signal certainly improves the data acquisition and reconstruction accuracy. But, in certain cases, the object structure is quite complex and it is difficultunder low signal-to-noise ratio (SNR) conditi polynomial function to match the energy dist ⁎ Corresponding authors. Tel.: +91 44 22575051.

E-mail addresses: jaganathanvee@gmail.com (J. Vella (R.R. Machireddy). http://dx.doi.org/10.1016/j.mri.2015.01.008 0730-725X/© 2015 Elsevier Inc. All rights reserved.

Please cite this article as: Vellagoundar J, M

Reson Imaging (2015), http://dx.doi.org/10ular sparse transform ved by random underistribution [4–6]. More

However, wavelet based sparse representation does not extend to piecewise smooth images. In recent times, prior knowledge of k-space amplitude profile and anatomical structures of objects aredomain. In MRI, incoherent aliasing is achie sampling of k-space according to its energy d1. Introduction

Compressive Sampling (CS) recons scans by reconstructing images from conventionally required. One of the identify an optimum k-space unders reconstruction of images. According reconstruction is accurate when a produces an incoherent aliasing in ahelps to speed upMRI k-space samples than nges in CS-MRI is to g pattern for accurate theory [1–3], image ersampled MR image is a difficult problem. To overcome this problem, k-space sampling procedure is considered as an optimization problem and is solved for an optimum sampling trajectory [10]. But the method is computationally intensive and time consuming.

For the images having sparse representation in wavelet domain, k-space samples are identified according to the significant wavelet coefficients [11]. This adaptive technique solves the above mentioned problems by exactly sampling the required k-space data.ons. However, tuning of ribution of the k-space function is extra associated with t compute a spectra of sampling patte such that the low k-space are sampl goundar), rsreddy@iitm.ac.in achireddy RR, A robust adaptive sampling m .1016/j.mri.2015.01.008tuning to compute k-spaceA robust adaptive samplingmethod for fas

Jaganathan Vellagoundar⁎, Ramasubba Reddy Mach

Biomedical Engineering Group, Department of Applied Mechanics, Indian Institute of Tec a b s t r a c ta r t i c l e i n f o

Article history:

Received 23 April 2014

Revised 19 October 2014

Accepted 10 January 2015

Available online xxxx

Keywords:

Adaptive sampling k-space sampling

Faster MR imaging

A robust adaptive k-space images. In this method, u acquired 2-D k-space da algorithm. Simulation exp various signal-to-noise ra variable density sampling m a fully acquired multi-slice 60% is achieved in the mu results show that reconstr j ourna l homepage:or acquisition ofMR images eddy ⁎ ogy Madras, India, 600 036 pling method is proposed for faster acquisition and reconstruction of MR ersampling patterns are generated based on magnitude profile of a fully

Images are reconstructed using compressive sampling reconstruction ents are done to assess the performance of the proposed method under (SNR) levels. The performance of the method is better than non-adaptive hod when k-space SNR is greater than 10 dB. Themethod is implemented on k-space data and a quality assurance phantom data. Data reduction of up to slice imaging data and 75% is achieved in the phantom imaging data. The on accuracy is improved over non-adaptive or conventional variable density ance Imaging w.mr i journa l .comcted from the data itself. There are few issues his method: (i) finding similar k-space data to l profile, (ii) the effect of noise in the computation rns, and (iii) controlling the sampling distribution frequency and the high frequency regions of ed sufficiently. Importantly, the last two issues will ethod for faster acquisition of MR images, Magn lice

M k-space Profile nte

Magnitude P ing 2 J. Vellagoundar, R.R. Machireddy / Magneticsignificantly affect the quality of reconstructed images. In this paper, we discussed a new adaptive sampling method to investigate the

Reconstructed

Image

Fig. 1. Flow diagram of the adaptive samplSlice-1 S k-space

Denoised Magnitude Segme

Any one of the slicesabove mentioned issues.

The objectives of the work are as follows: (i) to develop a sampling strategy based on a k-space magnitude profile of a fully sampled k-space, (ii) to compute sampling patterns which are free from the effect of noise (present in fully acquired k-space), and (iii) to simplify the overall sampling design. The new samplingmethod is tested on raw data of fully acquired 2-D multi-slice imaging and quality assurance phantom imaging. To study the effect of noise in the sampling pattern computation, simulation experiments are performed on noiseless MR images. Undersampling of k-space is done along phase encode direction of k-space (Cartesian sampling). 2. Theory