1 BME2012 in Vietnam, IFMBE Proceedings Vol.xxx, pp.xx, 2012 www.springerlink.com Application of l 1 Regularization for High-Quality Reconstruction of Ultrasound Tomography Tan Tran-Duc 1 , Nguyen Linh-Trung 1 , Michael L. Oelze 2 , and Minh N. Do 2 1 Fac. Electronics & Telecommunications, VNU University of Engineering & Technology, Hanoi, Vietnam 2 Dept. Electrical & Computer Engineering, University of Illinois at Urbana-Champaign,Urbana-Champaign,USA Abstract — Ultrasound tomography based on inverse scat- tering has the capability to resolve structures which are small- er than the wavelength of the incident wave, as opposed to conventional ultrasound imaging using echo method. Some material properties such as sound contrast are very useful to detect small objects. Born Iterative Method (BIM) based on first-order Born approximation has been introduced as an efficient diffraction tomography approach. However, this method has a high complexity because it has to solve large iterative forward and inverse problems. In this paper, we propose to replace Tikhonov regularization by l 1 -regularized least squares problem (LSP) in solving the inverse problem in BIM. As a result, the quality of reconstruction is improved and the complexity is reduced. Keywords— Ultrasound, tomography, inverse scattering, Born Iterative Method, Tikhonov regularization. I. INTRODUCTION AND STATE-OF-THE-ARTS Ultrasound imaging and tomography play important roles in clinical detection. Ultrasound image acquisition is mostly based on a pulse echo method that uses the time of light energy reflected by the boundaries of the object under imag- ing [2]. By extending the number of angles around the ob- ject, inverse scattering based techniques offer better quality of image reconstruction under strong scattering [2]. Works in ultrasound tomography often focus on calculat- ing the size of tissue (scattering area) and the speed of sound crossing the object being imaged. At present, there are only a few commercialized tomography devices. The reason is that state-of-the-art inverse scattering techniques have high computational complexity as well as limited effi- ciency. Born Iterative Method (BIM) and Distorted Born Iterative Method (DBIM) are well-known for diffraction tomography [1]. DBIM is more sensitive to noise, though it offers faster convergence as compared to that of BIM. In addition, the computational complexity of these methods is high due to their use of iterative forward and inverse processes. In [2], edge detection during the iterative process was introduced in order to speed up the convergence and to enhance the quality of reconstruction, but the complexity and noise sensitivity issues remain. In [3], the multi-level fast multi- pole algorithm (MLFMA) was applied to the forward solver for further speed up the reconstruction process. However, MLFMA requires high set-up costs that make it difficult to implement in practice. In conventional BIM, Tikhonov regularization (a.k.a., l 2 regularization) [4] was employed in solving the inverse problem. This method does not de-noise well, as we will later show in this paper. Based on this observation, we real- ize that if we solve the inverse problem well in terms of the speed and the quality of reconstruction, then we can reduce the number of the forward problem that follows in the itera- tive process. Thus, in this paper, we replace Tikhonov regu- larization by the l 1 -regularized least squares problem (LSP) [5]. We also show that this modification helps im- prove the quality of reconstruction and reduce the computa- tional complexity. II. MATERIALS AND METHODS A. Born Iterative Method (BIM) Fig. 1 schematically shows geometrical and acoustical configuration of the ultrasound tomography system. Fig. 1 Geometrical and acoustical configuration.