Application of Compressive Sensing to Ultrasound Images: A Review

Abstract

Compressive sensing (CS) offers compression of data below the Nyquist rate, making it an attractive solution in the field of medical imaging, and has been extensively used for ultrasound (US) compression and sparse recovery. In practice, CS offers a reduction in data sensing, transmission, and storage. Compressive sensing relies on the sparsity of data; i.e., data should be sparse in original or in some transformed domain. A look at the literature reveals that rich variety of algorithms have been suggested to recover data using compressive sensing from far fewer samples accurately, but with tradeoffs for efficiency. This paper reviews a number of significant CS algorithms used to recover US images from the undersampled data along with the discussion of CS in 3D US images. In this paper, sparse recovery algorithms applied to US are classified in five groups. Algorithms in each group are discussed and summarized based on their unique technique, compression ratio, sparsifying transform, 3D ultrasound, and deep learning. Research gaps and future directions are also discussed in the conclusion of this paper. This study is aimed to be beneficial for young researchers intending to work in the area of CS and its applications, specifically to US.

Trends in Compressive Sensing for EEG Signal Processing Applications

“…In the context of EEG signal for BCI application, mostly nonlinear algorithms are used, which require prior knowledge of sparsifying Ψ and A. Basically, the recovery of s in (3) from M compressed measurements, seeks for solution s by finding minimum few non-zero entries for an under-determined system N >> M. Mathematically, the recovery of s using l 0 -minimization is formulated as: s = arg min s s l 0 subject to : y = A s, (5) where s l 0 is the number of non-zero entries in s. A limitation of ( 5) is that it is NP-hard and ill-conditioned because of the non-convex nature of l 0 -minimization. However, (5) can be reformulated into a convex problem and a unique solution can be found by using l 1 -minimization given by ( 6)…”

Single Sensor Compressive Ultrasound Imaging: A Study of Affecting Factors

“…As US imaging techniques continue to advance, the number of transducer elements, data transmission rates (machine size), and processing rates (power consumption) all increase signi cantly [4]. As a result, the eld of compressive sensing (CS) [5] has emerged to address these challenges. CS provides a way to reconstruct a signal from sub-Nyquist sampled measurements by taking advantage of the signal's sparsity in a transformed domain [4][5][6].…”

“…As a result, the eld of compressive sensing (CS) [5] has emerged to address these challenges. CS provides a way to reconstruct a signal from sub-Nyquist sampled measurements by taking advantage of the signal's sparsity in a transformed domain [4][5][6]. While it is unlikely that CS techniques will challenge the high-quality images produced by conventional approaches in clinical settings, they may offer tangible bene ts in scenarios where machine size and hardware complexity are limited, such as in low-cost or space-constrained systems [6].…”

Trends in Compressive Sensing for EEG Signal Processing Applications

“…The theory of CS was initially proposed for low-rate image acquisition. It was then developed for many other applications such as ultrasound imaging [ 5 ], face recognition [ 6 , 7 ], single- pixel camera [ 8 ], wireless sensors networks [ 9 , 10 ], cognitive radio networks [ 11 , 12 ], sound localization [ 13 ], audio processing [ 14 , 15 ], radar imaging [ 16 , 17 ], image processing [ 18 , 19 ], and video processing [ 20 , 21 ]. Similarly, CS has contributed to various neural engineering research including, neuronal network connectivity [ 22 ], magnetic resonance image (MRI) acquisition [ 23 ], MRI reconstruction [ 24 ], electroencephalogram (EEG) monitoring [ 25 ], compressive imaging [ 26 , 27 ], and other applications.…”