Compressed Beamforming in Ultrasound Imaging

Abstract

Abstract-Emerging sonography techniques often require increasing the number of transducer elements involved in the imaging process. Consequently, larger amounts of data must be acquired and processed. The significant growth in the amounts of data affects both machinery size and power consumption. Within the classical sampling framework, state of the art systems reduce processing rates by exploiting the bandpass bandwidth of the detected signals. It has been recently shown, that a much more significant sample-rate reduction may be obtained, by treating ultrasound signals within the Finite Rate of Innovation framework. These ideas follow the spirit of Xampling, which combines classic methods from sampling theory with recent developments in Compressed Sensing. Applying such low-rate sampling schemes to individual transducer elements, which detect energy reflected from biological tissues, is limited by the noisy nature of the signals. This often results in erroneous parameter extraction, bringing forward the need to enhance the SNR of the low-rate samples. In our work, we achieve SNR enhancement, by beamforming the sub-Nyquist samples obtained from multiple elements. We refer to this process as "compressed beamforming". Applying it to cardiac ultrasound data, we successfully image macroscopic perturbations, while achieving a nearly eight-fold reduction in sample-rate, compared to standard techniques.

A Measurement Rate-MSE Tradeoff for Compressive Sensing Through Partial Support Recovery

“…as defined in (6). In practice one usually has no knowledge about the structure of w and thus γ needs to be chosen arbitrarily.…”

“…. , λ} with λ < k and γ opt λ as in (6). Equations (13)- (14) characterize the requirement for complete support recovery, whereas (15)- (16) Proof: The proof is provided in Appendix D-A.…”

Structurally random Fourier domain compressive sampling and frequency domain beamforming for ultrasound imaging

“…In recent years, the area of CS has branched out to a number of new fronts and has worked its way into several application areas, such as radar, communications, and ultrasound imaging. Eldar and her colleagues published extensively in applying CS theory to ultrasound imaging [4][5][6][7]. The key idea in all of these works is that the ultrasound signal can be modeled as Finite Rate of Innovation (FRI) signals which is a sum of a weighted and delayed known signal [8].…”

Greedy minimization of l1-norm with high empirical success

“…This has received much attention [1][2][3][4] and has several applications in signal processing [5][6][7][8][9]. One convex method for finding sparse representations is basis-pursuit [10] (or 1-minimization) which finds a sparse solution asx…”