In compressive sensing, the generalised orthogonal matching pursuit (gOMP) algorithm is one kind of sparse signal recovery algorithm, which generalises the OMP algorithm by selecting a fixed number of atoms at each iteration. Restricted isometry constant-based sufficient conditions to guarantee the correct support identification and the successful recovery of a sparse signal using the gOMP algorithm in a noiseless case are proposed. The proposed sufficient bounds are more relaxed compared with the existing ones.Introduction: Compressive sensing [1] deals with the sparse signal recovery from its insufficient linear measurement. The measurement signal can be expressed as y = Φx, where x ∈ R n × 1 , y ∈ R m × 1 and Φ ∈ R m × n are an original sparse signal, measurement signal and measurement matrix, respectively. There exists an infinite number of solutions to the measurement equation as m ≪ n which means that the linear equation is underdetermined. However, with the prior knowledge that x is sparse, the solution to the linear equation is unique. Various algorithms were successively proposed to recover sparse signal x. Basically, conditions to guarantee the success of the algorithms are expressed via the 'restricted isometry constant' (RIC), which could be defined as the smallest value δ K (0 < δ K < 1) that makes the following inequalities true [1]:

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Abstract. Mean scatterer spacing (MSS) estimated from ultrasonic backscattering is of valuable information for tissue characterization. However, low ultrasound frequency, sound attenuation, and diffuse scattering significantly disturb the current MSS measurement methods. The aim of this study is to improve MSS measurement with Coded Excitation (CE) enhanced cepstrum estimation. The study proposes a Golay code-based cepstrum estimation and uses an equivalent Faran cylinder model of cancellous bone. By solving the elastic wave equation, ultrasonic backscattering signals were obtained through simulations. The adopted ultrasonic excitation is 0.9 MHz and is coded with 4-bit complementary sequences, which is modulated by employing a sinusoidal signal. Also, white Gaussian noise of 60 dB, 55 dB, and 45 dB was added to the backscattering data to study the robustness of the proposed method. Simulation results show that the Golay-based method successfully improved ultrasound energy transmission into the tissue and effectively suppressed interference peaks while identifying the right peaks with permitted errors. In addition, the robustness against noise was enhanced.

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Physiological effects caused by power ultrasound radiation are of therapeutic benefits for fracture healing. However, these effects are hard to detect with current instrumentations. The aim of this paper is to analyze the behavior of bone subject to therapeutic ultrasound and provide data reference for an intelligent bone ultrasonic system. In this paper, we adopted a 3-D finite element method as a virtual measurement tool to study the acoustic-radiation-induced stress fields inside and on the surface of bone. The equivalent long bone model was built and the soft tissue was involved by establishing coupling connections with bone surface points. The ultrasound radiation was generated by a 2-MHz excitation and was applied on the surface of soft tissue. In this paper, we first defined six paths in different bone layers to quantitatively study the longitudinal stress distribution and examined the concentration center positions and width with sliding windows. Then, the circumferential stress evolution from relaxation fields to concentration fields was investigated by computing the stress fields on cross sections. Analytical dispersion curves were measured to characterize the guided wave modes. The results show that the middle bone tissue has a higher mean stress (2027.7 Pa) than the surface (763.3 Pa) and the outer bone layer (1898.1 Pa), and the stress distribution of the middle layer is less disturbed (coefficient of variation = 39.8%). Also, on cross section of the concentration zones, periodical fields with a distance of half-wavelength are obtained. From 0.2 to 2 MHz, the acoustic intensity grows proportionally with excitation amplitude.Index Terms-Bone, finite element method (FEM), intelligent system, stress field, therapeutic ultrasound.