Numerous physiological processes are cyclical, but sampling these processes densely enough to perform frequency decomposition and subsequent analyses can be challenging. Mathematical approaches for decomposition and reconstruction of sparsely and irregularly sampled signals are well established but have been under-utilized in physiological applications. We developed a basis pursuit denoising with polynomial detrending (BPWP) model that recovers oscillations and trends from sparse and irregularly sampled timeseries. We validated this model on a unique dataset of long-term inter-ictal epileptiform discharge (IED) rates from human hippocampus recorded with a novel investigational device with continuous local field potential sensing. IED rates have well established circadian and multiday cycles related to sleep, wakefulness, and seizure clusters. Given sparse and irregular samples of IED rates from multi-month intracranial EEG recordings from ambulatory humans, we used BPWP to compute narrowband spectral power and polynomial trend coefficients and identify IED rate cycles in three subjects. In select cases, we propose that random and irregular sampling may be leveraged for frequency decomposition of physiological signals. Trial Registration: NCT03946618.

Ultrasound localization microscopy (ULM) based on microbubble (MB) localization was recently introduced to overcome the resolution limit of conventional ultrasound. However, ULM is currently challenged by the requirement for long data acquisition times to accumulate adequate MB events to fully reconstruct vasculature. In this study, we present a curvelet transform-based sparsity promoting (CTSP) algorithm that improves ULM imaging speed by recovering missing MB localization signal from data with very short acquisition times. CTSP was first validated in a simulated microvessel model, followed by the chicken embryo chorioallantoic membrane (CAM), and finally, in the mouse brain. In the simulated microvessel study, CTSP robustly recovered the vessel model to achieve an 86.94% vessel filling percentage from a corrupted image with only 4.78% of the true vessel pixels. In the chicken embryo CAM study, CTSP effectively recovered the missing MB signal within the vasculature, leading to marked improvement in ULM imaging quality with a very short data acquisition. Taking the optical image as reference, the vessel filling percentage increased from 2.7% to 42.2% using 50ms of data acquisition after applying CTSP. CTSP used 80% less time to achieve the same 90% maximum saturation level as compared with conventional MB localization. We also applied CTSP on the microvessel flow speed maps and found that CTSP was able to use only 1.6s of microbubble data to recover flow speed images that have similar qualities as those constructed using 33.6s of data. In the mouse brain study, CTSP was able to reconstruct the majority of the cerebral vasculature using 1-2s of data acquisition. Additionally, CTSP only needed 3.2s of microbubble data to generate flow velocity maps that are comparable to those using 129.6s of data. These results suggest that CTSP can facilitate fast and robust ULM imaging especially under the circumstances of inadequate microbubble localizations.

Shear wave elastography methods are able to accurately measure tissue stiffness, allowing these techniques to monitor the progression of hepatic fibrosis. While many methods rely on acoustic radiation force to generate shear waves for 2-D imaging, probe oscillation shear wave elastography (PROSE) provides an alternative approach by generating shear waves through continuous vibration of the ultrasound probe while simultaneously detecting the resulting motion. The generated shear wave field in in vivo liver is complicated, and the amplitude and quality of these shear waves can be influenced by the placement of the vibrating probe. To address these challenges, a real-time shear wave visualization tool was implemented to provide instantaneous visual feedback to optimize probe placement. Even with the real-time display, it was not possible to fully suppress residual motion with established filtering methods. To solve this problem, the shear wave signal in each frame was decoupled from motion and other sources through the use of a parameter-free empirical mode decomposition before calculating shear wave speeds. This method was evaluated in a phantom as well as in in vivo livers from five volunteers. PROSE results in the phantom as well as in vivo liver correlated well with independent measurements using the commercial General Electric Logiq E9 scanner.

We consider the problem of modeling data matrices with locally low rank (LLR) structure, a generalization of the popular low rank structure widely used in a variety of real world application domains ranging from medical imaging to recommendation systems. While LLR modeling has been found to be promising in real world application domains, limited progress has been made on the design of scalable algorithms for such structures. In this paper, we consider a convex relaxation of LLR structure, and propose an efficient algorithm based on dual projected gradient descent (D-PGD) for computing the proximal operator. While the original problem is non-smooth, so that primal (sub)gradient algorithms will be slow, we show that the proposed D-PGD algorithm has geometrical convergence rate. We present several practical ways to further speed up the computations, including acceleration and approximate SVD computations. With experiments on both synthetic and real data from MRI (magnetic resonance imaging) denoising, we illustrate the superior performance of the proposed D-PGD algorithm compared to several baselines.

Robust clutter filtering is essential for ultrasound small vessel imaging. Eigen-based clutter filtering techniques have recently shown great improvement in clutter rejection over conventional clutter filters in small animals. However, for in vivo human imaging, eigen-based clutter filtering can be challenging due to the complex spatially-varying tissue and noise characteristics. To address this challenge, we present a novel block-wise adaptive singular value decomposition (SVD) based clutter filtering technique. The proposed method divides the global plane wave data into overlapped local spatial segments, within which tissue signals are assumed to be locally coherent and noise locally stationary. This, in turn, enables effective separation of tissue, blood and noise via SVD. For each block, the proposed method adaptively determines the singular value cutoff thresholds based on local data statistics. Processing results from each block are redundantly combined to improve both the signal-to-noise-ratio (SNR) and the contrast-to-noise-ratio (CNR) of the small vessel perfusion image. Experimental results show that the proposed method achieved more than two-fold increase in SNR and more than three-fold increase in CNR in dB scale over the conventional global SVD filtering technique for an in vivo human native kidney study. The proposed method also showed substantial improvement in suppression of the depth-dependent background noise and better rejection of near field tissue clutter. The effects of different processing block size and block overlap percentage were systematically investigated as well as the tradeoff between imaging quality and computational cost.

The Non-Uniform Fast Fourier Transform (NUFFT) is a generalization of FFT to non-equidistant samples. It has many applications which vary from medical imaging to radio astronomy to the numerical solution of partial differential equations. Despite recent advances in speeding up NUFFT on various platforms, its practical applications are still limited, due to its high computational cost, which is significantly dominated by the convolution of a signal between a non-uniform and uniform grids. The computational cost of the NUFFT is particularly detrimental in cases which require fast reconstruction times, such as iterative 3D non-Cartesian MRI reconstruction. We propose novel and highly scalable parallel algorithm for performing NUFFT on x86-based multi-core CPUs. The high performance of our algorithm relies on good SIMD utilization and high parallel efficiency. On convolution, we demonstrate on average 90% SIMD efficiency using SSE, as well up to linear scalability using a quad-socket 40-core Intel(R) Xeon(R) E7-4870 Processors based system. As a result, on dual socket Intel(R) Xeon(R) X5670 based server, our NUFFT implementation is more than 4x faster compared to the best available NUFFT3D implementation, when run on the same hardware. On Intel(R) Xeon(R) E5-2670 processor based server, our NUFFT implementation is 1.5X faster than any published NUFFT implementation today. Such speed improvement opens new usages for NUFFT. For example, iterative multi channel reconstruction of a 240×240×240 image could execute in just over 3 minutes, which is on the same order as contemporary non-iterative (and thus less-accurate) 3D NUFFT-based MRI reconstructions.

In clinical magnetic resonance imaging (MRI), any reduction in scan time offers a number of potential benefits ranging from high-temporal-rate observation of physiological processes to improvements in patient comfort. Following recent developments in compressive sensing (CS) theory, several authors have demonstrated that certain classes of MR images which possess sparse representations in some transform domain can be accurately reconstructed from very highly undersampled K-space data by solving a convex l(1) -minimization problem. Although l(1)-based techniques are extremely powerful, they inherently require a degree of over-sampling above the theoretical minimum sampling rate to guarantee that exact reconstruction can be achieved. In this paper, we propose a generalization of the CS paradigm based on homotopic approximation of the l(0) quasi-norm and show how MR image reconstruction can be pushed even further below the Nyquist limit and significantly closer to the theoretical bound. Following a brief review of standard CS methods and the developed theoretical extensions, several example MRI reconstructions from highly undersampled K-space data are presented.