IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, . 60, . 11, NOVEMBER 2013 2266 0885–3010/$25.00 © 2013 IEEE Phase-Based Direct Average Strain Estimation for Elastography Sharmin R. Ara, Faisal Mohsin, Farzana Alam, Sharmin Akhtar Rupa, Rayhana Awwal, Soo Yeol Lee, and Md. Kamrul Hasan Abstract—In this paper, a phase-based direct average strain estimation method is developed. A mathematical model is pre- sented to calculate axial strain directly from the phase of the zero-lag cross-correlation function between the windowed pre- compression and stretched post-compression analytic signals. Unlike phase-based conventional strain estimators, for which strain is computed from the displacement field, strain in this paper is computed in one step using the secant algorithm by exploiting the direct phase–strain relationship. To maintain strain continuity, instead of using the instantaneous phase of the interrogative window alone, an average phase function is defined using the phases of the neighboring windows with the assumption that the strain is essentially similar in a close physical proximity to the interrogative window. This method accounts for the effect of lateral shift but without requiring a prior estimate of the applied strain. Moreover, the strain can be computed both in the compression and relaxation phases of the applied pressure. The performance of the proposed strain estimator is analyzed in terms of the quality metrics elasto- graphic signal-to-noise ratio (SNRe), elastographic contrast-to- noise ratio (CNRe), and mean structural similarity (MSSIM), using a finite element modeling simulation phantom. The re- sults reveal that the proposed method performs satisfactorily in terms of all the three indices for up to 2.5% applied strain. Comparative results using simulation and experimental phan- tom data, and in vivo breast data of benign and malignant masses also demonstrate that the strain image quality of our method is better than the other reported techniques. I. I E  is an imaging modality for noninvasive assessment of tissue elasticity by measuring its degree of deformation under the application of an external force. Tissue elasticity, a mechanical characteristic which may change under the influence of pathophysiologic processes, has clinical benefit in the diagnostic evaluation of differ- ent diseased organs [1]–[5]. Elastography provides a quan- titative evaluation of the elastic parameter of tissue and promises detection of pathological changes at the primary stage for diagnosing breast cancer [6]–[8], prostate cancer [9], liver cirrhosis [10], vascular plaques [11], and lymph node and thyroid cancer [12], [13]. In quasi-static elastography, the time-domain post- compression RF signal is modeled as a compressed and delayed version of the pre-compression RF signal. To ascertain the displacement between these two signals, which is eventually used to calculate strain, the correla- tion of these pre- and post-compression signals are ana- lyzed. Algorithms based on this principle are categorized as displacement-based strain estimation techniques. Some of the notable displacement-based strain estimators are time delay estimation (TDE) [6], [8], [14], time delay es- timation with prior estimate (TDPE) [15], and analytic minimization (AM) [16]. TDE fails at high strain because of decorrelation noise and is unsuitable for real-time ap- plication because of its high computational cost. TDPE is an improved version of TDE, in which prior estimates from the neighboring windows are used for reducing the search region of the correlation peak. At high strain, when the correlation falls below a predefined threshold, TDPE switches to TDE. TDPE, however, suffers from the noise introduced by the gradient operator in calculating strain from the displacement field, which is recognized as a ma- jor drawback of the gradient-based algorithms. All of these windowing approaches must trade-off between the good spatial resolution of small windows and the accuracy of large windows which help to reduce jitter errors [16]. Ana- lytic minimization (AM) [16] uses an individual sample of RF data, omitting the window-based analysis. The effect of decorrelation noise is minimized in this real-time 2-D elastography technique through the use of regularization terms. However, 2-D analytic minimization (AM2D) is highly sensitive to the optimal setting of eight tuning pa- rameters and attenuation effects. Another group of algo- rithms known as direct strain estimators [17]–[20] employ global or local adaptive scaling of the post-compression signal to estimate strain directly from the stretching fac- tor. Strain estimation using the neighborhood in [20] was based on a Fourier spectrum equalization technique where the mean strain at the interrogative window was com- puted by minimizing, with respect to stretching factor, a cost function derived from the exponentially weighted windowed segments in both the axial and lateral direc- Manuscript received February 26, 2013; accepted August 7, 2013. This work was supported by the Higher Education Quality Enhancement Program (HEQEP), University Grants Commission (UGC) (CP#96/ BUET/Win-2/ST(EEE)/2010), Bangladesh, and in part by National Research Foundation of Korea grant funded by the Korean government (2009-0078310). S. R. Ara, F. Mohsin, and M. K. Hasan are with the Department of Electrical and Electronic Engineering, Bangladesh University of Engi- neering and Technology (BUET), Dhaka, Bangladesh (e-mail: khasan@ eee.buet.ac.bd). F. Alam is with the Department of Radiology and Imaging, Bang- abandhu Sheikh Mujib Medical University (BSMMU), Dhaka, Bangla- desh. S. A. Rupa is with the Department of Radiology and Imaging, Enam Medical College and Hospital, Savar, Dhaka, Bangladesh. R. Awwal is with the Department of Plastic Surgery, Dhaka Medical College, Dhaka, Bangladesh. S. Y. Lee and M. K. Hasan are with the Department of Biomedi- cal Engineering, Kyung Hee University, Kyungki, South Korea (e-mail: sylee01@khu.ac.kr). DOI http://dx.doi.org/10.1109/TUFFC.2013.2825