Frequency Domain Compressive Sampling for Ultrasound Imaging

Abstract

Compressed sensing or compressive sampling is a recent theory that originated in the applied mathematics field. It suggests a robust way to sample signals or images below the classic Shannon-Nyquist theorem limit. This technique has led to many applications, and has especially been successfully used in diverse medical imaging modalities such as magnetic resonance imaging, computed tomography, or photoacoustics. This paper first revisits the compressive sampling theory and then proposes several strategies to perform compressive sampling in the context of ultrasound imaging. Finally, we show encouraging results in 2D and 3D, on high- and low-frequency ultrasound images.

A Sparse Reconstruction Framework for Fourier-Based Plane-Wave Imaging

“…In the context of ultrasonic imaging, several studies have already exploited the sparsity of backscattered echo signals in the wave atom frame [30], as well as of radio frequency images in specific frames such as 2D Fourier basis [31], wavelet basis [32], or even learned dictionaries [33]. Schiffner et al introduced CS-based plane wave beamforming in the frequency domain assuming sparsity in an orthonormal wavelet basis [34] while Chernyakova et al used a Xampling scheme and a finite rate of innovation model to achieve CS-based Fourier beamforming [35].…”

Compressed Sensing Techniques for Ultrasonic Imaging of Cargo Containers

“…Note that although only 36% of the samples are selected, there is at least one selected spatial sample for each frequency, and vice-versa. As discussed in [11][12][13]29], while random sensing matrices minimize the coherence of Θ = Φ , it must be taken into account that physical limitations of the data acquisition system in which CS is going to be applied, may prevent random sampling from being advantageous, with respect to conventional sampling at a Nyquist rate. Considering this, [11] analyzes several sampling patterns, proposed as a trade-off between maximizing the incoherence of Θ (random sampling), and the practical implementation of the acquisition system (partial random sampling).…”

Compressive-sensing-based multidimensional Doppler signal analysis for fetal activity monitoring

“…As we have explained previously, one of the key points in the CS framework is the sparsity assumption of the signals to recover. Herein, we consider the 2D Fourier transform (F) of X to be sparse [19]. The recovery of the Doppler signals follows the optimization process in (6).…”