Variable Density Random Sampling Research Articles

Enhancing in full-color single-pixel imaging: integrating variable density sampling with hyper-Laplacian priors

Full-color single-pixel imaging aims to restore chromatic images using a single detector element, such as a photodiode or a single-pixel camera. However, image quality is inevitably compromised at low sampling rates due to inefficient sampling methods or incomplete representation of spectrum information. To address these challenges, we meticulously consider the distribution of the image frequency spectrum and the correlation between multiple bands and make further improvements in sampling strategy and reconstruction methods. First, we propose a variable density random sampling strategy based on the exponential distribution to enhance image sampling efficiency. Second, we discover that in most cases, there exists a hyper-Laplacian distribution between spectral mixed images and monochromatic images. Building upon this observation, we designed a hyper-Laplacian prior and seamlessly integrated it into our reconstruction method to enhance the performance of full-color images. Experimental results demonstrate that our method significantly improves the quality of reconstructed full-color images compared to state-of-the-art methods.

Fast and high-quality single-pixel imaging.

The imaging quality of the conventional single-pixel-imaging (SPI) technique seriously degrades at a low sampling rate. To tackle this problem, we propose an efficient sampling method and a high-quality real-time image reconstruction strategy: first, different from the conventional simple circular path sampling strategy or variable density random sampling technique, the proposed method samples the Fourier spectrum using the spectrum distribution of the image, that is, sampling the significant spectrum coefficients first, which will help to improve the image quality at a relevantly low sampling rate; second, to handle the long image reconstruction time caused by the iterative algorithm, the sparsity of the image and the alternating direction optimization strategy are combined to ameliorate the reconstruction process in the image gradient space. Compared with the state-of-the-art techniques, the proposed method significantly improves the imaging quality and achieves real-time reconstruction on the time scale of milliseconds.

Accelerating whole-heart 3D T2 mapping: Impact of undersampling strategies and reconstruction techniques.

PurposeWe aim to determine an advantageous approach for the acceleration of high spatial resolution 3D cardiac T2 relaxometry data by comparing the performance of different undersampling patterns and reconstruction methods over a range of acceleration rates.MethodsMulti-volume 3D high-resolution cardiac images were acquired fully and undersampled retrospectively using 1) optimal CAIPIRINHA and 2) a variable density random (VDR) sampling. Data were reconstructed using 1) multi-volume sensitivity encoding (SENSE), 2) joint-sparsity SENSE and 3) model-based SENSE. Four metrics were calculated on 3 naïve swine and 8 normal human subjects over a whole left-ventricular region of interest: root-mean-square error (RMSE) of image signal intensity, RMSE of T2, the bias of mean T2, and standard deviation (SD) of T2. Fully sampled data and volume-by-volume SENSE with standard equally spaced undersampling were used as references. The Jaccard index calculated from one swine with acute myocardial infarction (MI) was used to demonstrate preservation of segmentation of edematous tissues with elevated T2.ResultsIn naïve swine and normal human subjects, all methods had similar performance when the net reduction factor (Rnet) <2.5. VDR sampling with model-based SENSE showed the lowest RMSEs (10.5%-14.2%) and SDs (+1.7–2.4 ms) of T2 when Rnet>2.5, while VDR sampling with the joint-sparsity SENSE had the lowest bias of mean T2 (0.0–1.1ms) when Rnet>3. The RMSEs of parametric T2 values (9.2%-24.6%) were larger than for image signal intensities (5.2%-18.4%). In the swine with MI, VDR sampling with either joint-sparsity or model-based SENSE showed consistently higher Jaccard index for all Rnet (0.71–0.50) than volume-by-volume SENSE (0.68–0.30).ConclusionsRetrospective exploration of undersampling and reconstruction in 3D whole-heart T2 parametric mapping revealed that maps were more sensitive to undersampling than images, presenting a more stringent limiting factor on Rnet. The combination of VDR sampling patterns with model-based or joint-sparsity SENSE reconstructions were more robust for Rnet>3.

Compressed sensing velocity encoded phase contrast imaging: Monitoring skeletal muscle kinematics.

This study implements a compressed sensing (CS) 3-directional velocity encoded phase contrast (VE-PC) imaging for studying skeletal muscle kinematics within 40 s. Independent variable density random sampling in the phase encoding direction for each temporal frame was implemented for various combinations of CS-factors and views per segment. CS reconstruction was performed for the combined multicoil, temporal datasets using temporal Fourier transform followed by temporal principal component analysis sparsifying transformations. The method was tested on a flow phantom and in vivo, on velocity and strain rate of the medial gastrocnemius muscle of 11 subjects performing isometric contractions. For the flow phantom, velocity from 8 undersampled sequences matched very well with the flowmeter values over a range of velocities spanning in vivo muscle velocities. Bland-Altman plots of the peak strain rate eigenvalues comparing 7 undersampled sequences was in good agreement with the reference (full k-space) scan. CS-factor of 4 combined with views per segment of 4 (scan times reduced by 4) yielded images with no visual artifacts allowing and yielded velocities and strain rate maps in the lower leg muscle in 40 s. This study shows that a reduction in scan time of velocity encoded phase contrast imaging up to a factor of 4 is possible using the proposed CS reconstruction.

Sparse Fourier single-pixel imaging.

Fourier single-pixel imaging is one of the main single-pixel imaging techniques. To improve the imaging efficiency, some of the recent method typically select the low-frequency and discard the high-frequency information to reduce the number of acquired samples. However, sampling only a small amount of low-frequency components will lead to the loss of object details and will reduce the imaging resolution. At the same time, the ringing effect of the restored image due to frequency truncation is significant. In this paper, a new sparse Fourier single-pixel imaging method is proposed that reduces the number of samples explorations while maintaining increased image quality. The proposed method makes a special use of the characteristics of the Fourier spectrum distribution based on which the power of image information decreases gradually from low to high frequencies in the Fourier space. A variable density random sampling matrix is employed to achieve random sampling with Fourier single-pixel imaging technology, followed by the processing of the sparse Fourier spectra using compressive sensing algorithms to recover the high-quality information of the object. The new algorithm can effectively improve the quality of object restoration comparing with the existing Fourier single-pixel imaging methods which only acquire the low-frequency parts. Additionally, considering that the resolution of the system is diffraction limited, super-resolution imaging can also be achieved. Experimental results demonstrate the mainly correctness but also effectiveness of the proposed method.

Unified Theory for Recovery of Sparse Signals in a General Transform Domain

Compressed sensing is provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that the practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many real-world applications, a signal of interest is typically sparse not in the canonical basis but in a certain transform domain, such as wavelets or the finite difference. The theory of compressed sensing was extended to the analysis sparsity model, but known extensions are limited to the specific choices of sensing matrix and sparsifying transform. In this paper, we propose a unified theory for robust recovery of sparse signals in a general transform domain by convex programming. In particular, our results apply to the general acquisition and sparsity models and show how the number of measurements for recovery depends on properties of measurement and sparsifying transforms. Moreover, we also provide extensions of our results to the scenarios where the atoms in the transform have varying incoherence parameters and the unknown signal exhibits a structured sparsity pattern. In particular, for the partial Fourier recovery of sparse signals over a circulant transform, our main results suggest a uniformly random sampling. Numerical results demonstrate that the variable density random sampling by our main results provides a superior recovery performance over the known sampling strategies.

Variable density incoherent spatiotemporal acquisition (VISTA) for highly accelerated cardiac MRI.

For the application of compressive sensing to parallel MRI, Poisson disk sampling (PDS) has been shown to generate superior results compared with random sampling methods. However, due to its limited flexibility to incorporate additional constraints, PDS is not readily extendible to dynamic applications. Here, we propose and validate a pseudo-random sampling technique that allows incorporating constraints specific to dynamic imaging. The proposed sampling scheme, called variable density incoherent spatiotemporal acquisition (VISTA), is based on constrained minimization of Riesz energy on a spatiotemporal grid. Data from both a digital phantom and real-time cine were used to compare VISTA with uniform interleaved sampling (UIS) and variable density random sampling (VRS). The image quality was assessed qualitatively and quantitatively. VISTA improved the trade-off between noise and sharpness. Also, VISTA produced diagnostic quality images at an acceleration rate of 15, whereas UIS and VRS images degraded below the diagnostic threshold at lower acceleration rates. VISTA generates spatiotemporal sampling patterns with high levels of uniformity and incoherence, while maintaining a constant temporal resolution. Using a small pilot study, VISTA was shown to produce diagnostic quality images at acceleration rates up to 15.

Adaptive k-space sampling design for edge-enhanced DCE-MRI using compressed sensing

The critical challenge in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is the trade-off between spatial and temporal resolution due to the limited availability of acquisition time. To address this, it is imperative to under-sample k-space and to develop specific reconstruction techniques. Our proposed method reconstructs high-quality images from under-sampled dynamic k-space data by proposing two main improvements; i) design of an adaptive k-space sampling lattice and ii) edge-enhanced reconstruction technique. A high-resolution data set obtained before the start of the dynamic phase is utilized. The sampling pattern is designed to adapt to the nature of k-space energy distribution obtained from the static high-resolution data. For image reconstruction, the well-known compressed sensing-based total variation (TV) minimization constrained reconstruction scheme is utilized by incorporating the gradient information obtained from the static high-resolution data. The proposed method is tested on seven real dynamic time series consisting of 2 breast data sets and 5 abdomen data sets spanning 1196 images in all. For data availability of only 10%, performance improvement is seen across various quality metrics. Average improvements in Universal Image Quality Index and Structural Similarity Index Metric of up to 28% and 24% on breast data and about 17% and 9% on abdomen data, respectively, are obtained for the proposed method as against the baseline TV reconstruction with variable density random sampling pattern.

Adapted random sampling patterns for accelerated MRI

Variable density random sampling patterns have recently become increasingly popular for accelerated imaging strategies, as they lead to incoherent aliasing artifacts. However, the design of these sampling patterns is still an open problem. Current strategies use model assumptions like polynomials of different order to generate a probability density function that is then used to generate the sampling pattern. This approach relies on the optimization of design parameters which is very time consuming and therefore impractical for daily clinical use. This work presents a new approach that generates sampling patterns by making use of power spectra of existing reference data sets and hence requires neither parameter tuning nor an a priori mathematical model of the density of sampling points. The approach is validated with downsampling experiments, as well as with accelerated in vivo measurements. The proposed approach is compared with established sampling patterns, and the generalization potential is tested by using a range of reference images. Quantitative evaluation is performed for the downsampling experiments using RMS differences to the original, fully sampled data set. Our results demonstrate that the image quality of the method presented in this paper is comparable to that of an established model-based strategy when optimization of the model parameter is carried out and yields superior results to non-optimized model parameters. However, no random sampling pattern showed superior performance when compared to conventional Cartesian subsampling for the considered reconstruction strategy.