Compressive hyperspectral imaging via adaptive sampling and dictionary learning

In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using dictionary learning. We then perform an SVD on the dictionary and use the first few left singular vectors as the rows of the measurement matrix to obtain the compressive measurements for reconstruction. The proposed method provides significant improvement over the conventional compressive sensing approaches. The reconstruction performance is further improved by reconditioning the sensing matrix using matrix balancing. We also demonstrate that the combination of dictionary learning and SVD is robust by applying them to different datasets

Data-Driven Learning of a Union of Sparsifying Transforms Model for Blind Compressed Sensing

Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying sparse signal model is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the unknown model from highly undersampled measurements. Specifically, our model is that the patches of the underlying image(s) are approximately sparse in a transform domain. We also extend this model to a union of transforms model that better captures the diversity of features in natural images. The proposed block coordinate descent type algorithms for blind compressed sensing are highly efficient, and are guaranteed to converge to at least the partial global and partial local minimizers of the highly non-convex BCS problems. Our numerical experiments show that the proposed framework usually leads to better quality of image reconstructions in MRI compared to several recent image reconstruction methods. Importantly, the learning of a union of sparsifying transforms leads to better image reconstructions than a single adaptive transform.Comment: Appears in IEEE Transactions on Computational Imaging, 201

Sparse-View X-Ray CT Reconstruction Using ℓ1\ell_1 Prior with Learned Transform

A major challenge in X-ray computed tomography (CT) is reducing radiation dose while maintaining high quality of reconstructed images. To reduce the radiation dose, one can reduce the number of projection views (sparse-view CT); however, it becomes difficult to achieve high-quality image reconstruction as the number of projection views decreases. Researchers have applied the concept of learning sparse representations from (high-quality) CT image dataset to the sparse-view CT reconstruction. We propose a new statistical CT reconstruction model that combines penalized weighted-least squares (PWLS) and $\ell_1$ prior with learned sparsifying transform (PWLS-ST-$\ell_1$), and a corresponding efficient algorithm based on Alternating Direction Method of Multipliers (ADMM). To moderate the difficulty of tuning ADMM parameters, we propose a new ADMM parameter selection scheme based on approximated condition numbers. We interpret the proposed model by analyzing the minimum mean square error of its ($\ell_2$-norm relaxed) image update estimator. Our results with the extended cardiac-torso (XCAT) phantom data and clinical chest data show that, for sparse-view 2D fan-beam CT and 3D axial cone-beam CT, PWLS-ST-$\ell_1$ improves the quality of reconstructed images compared to the CT reconstruction methods using edge-preserving regularizer and $\ell_2$ prior with learned ST. These results also show that, for sparse-view 2D fan-beam CT, PWLS-ST-$\ell_1$ achieves comparable or better image quality and requires much shorter runtime than PWLS-DL using a learned overcomplete dictionary. Our results with clinical chest data show that, methods using the unsupervised learned prior generalize better than a state-of-the-art deep "denoising" neural network that does not use a physical imaging model.Comment: The first two authors contributed equally to this wor

Robust X-ray Sparse-view Phase Tomography via Hierarchical Synthesis Convolutional Neural Networks

Convolutional Neural Networks (CNN) based image reconstruction methods have been intensely used for X-ray computed tomography (CT) reconstruction applications. Despite great success, good performance of this data-based approach critically relies on a representative big training data set and a dense convoluted deep network. The indiscriminating convolution connections over all dense layers could be prone to over-fitting, where sampling biases are wrongly integrated as features for the reconstruction. In this paper, we report a robust hierarchical synthesis reconstruction approach, where training data is pre-processed to separate the information on the domains where sampling biases are suspected. These split bands are then trained separately and combined successively through a hierarchical synthesis network. We apply the hierarchical synthesis reconstruction for two important and classical tomography reconstruction scenarios: the spares-view reconstruction and the phase reconstruction. Our simulated and experimental results show that comparable or improved performances are achieved with a dramatic reduction of network complexity and computational cost. This method can be generalized to a wide range of applications including material characterization, in-vivo monitoring and dynamic 4D imaging.Comment: 9 pages, 6 figures, 2 table

Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT

X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-Net have demonstrated impressive performance for sparse- view CT reconstruction. However, theoretical justification is still lacking. Inspired by the recent theory of deep convolutional framelets, the main goal of this paper is, therefore, to reveal the limitation of U-Net and propose new multi-resolution deep learning schemes. In particular, we show that the alternative U- Net variants such as dual frame and the tight frame U-Nets satisfy the so-called frame condition which make them better for effective recovery of high frequency edges in sparse view- CT. Using extensive experiments with real patient data set, we demonstrate that the new network architectures provide better reconstruction performance.Comment: This will appear in IEEE Transaction on Medical Imaging, a special issue of Machine Learning for Image Reconstructio

Convolutional Sparse Coding for Compressed Sensing CT Reconstruction

Over the past few years, dictionary learning (DL)-based methods have been successfully used in various image reconstruction problems. However, traditional DL-based computed tomography (CT) reconstruction methods are patch-based and ignore the consistency of pixels in overlapped patches. In addition, the features learned by these methods always contain shifted versions of the same features. In recent years, convolutional sparse coding (CSC) has been developed to address these problems. In this paper, inspired by several successful applications of CSC in the field of signal processing, we explore the potential of CSC in sparse-view CT reconstruction. By directly working on the whole image, without the necessity of dividing the image into overlapped patches in DL-based methods, the proposed methods can maintain more details and avoid artifacts caused by patch aggregation. With predetermined filters, an alternating scheme is developed to optimize the objective function. Extensive experiments with simulated and real CT data were performed to validate the effectiveness of the proposed methods. Qualitative and quantitative results demonstrate that the proposed methods achieve better performance than several existing state-of-the-art methods.Comment: Accepted by IEEE TM

A Compressed Sensing Algorithm for Sparse-View Pinhole Single Photon Emission Computed Tomography

Single Photon Emission Computed Tomography (SPECT) systems are being developed with multiple cameras and without gantry rotation to provide rapid dynamic acquisitions. However, the resulting data is angularly undersampled, due to the limited number of views. We propose a novel reconstruction algorithm for sparse-view SPECT based on Compressed Sensing (CS) theory. The algorithm models Poisson noise by modifying the Iterative Hard Thresholding algorithm to minimize the Kullback-Leibler (KL) distance by gradient descent. Because the underlying objects of SPECT images are expected to be smooth, a discrete wavelet transform (DWT) using an orthogonal spline wavelet kernel is used as the sparsifying transform. Preliminary feasibility of the algorithm was tested on simulated data of a phantom consisting of two Gaussian distributions. Single-pinhole projection data with Poisson noise were simulated at 128, 60, 15, 10, and 5 views over 360 degrees. Image quality was assessed using the coefficient of variation and the relative contrast between the two objects in the phantom. Overall, the results demonstrate preliminary feasibility of the proposed CS algorithm for sparse-view SPECT imaging

Depth Reconstruction from Sparse Samples: Representation, Algorithm, and Sampling

The rapid development of 3D technology and computer vision applications have motivated a thrust of methodologies for depth acquisition and estimation. However, most existing hardware and software methods have limited performance due to poor depth precision, low resolution and high computational cost. In this paper, we present a computationally efficient method to recover dense depth maps from sparse measurements. We make three contributions. First, we provide empirical evidence that depth maps can be encoded much more sparsely than natural images by using common dictionaries such as wavelets and contourlets. We also show that a combined wavelet-contourlet dictionary achieves better performance than using either dictionary alone. Second, we propose an alternating direction method of multipliers (ADMM) to achieve fast reconstruction. A multi-scale warm start procedure is proposed to speed up the convergence. Third, we propose a two-stage randomized sampling scheme to optimally choose the sampling locations, thus maximizing the reconstruction performance for any given sampling budget. Experimental results show that the proposed method produces high quality dense depth estimates, and is robust to noisy measurements. Applications to real data in stereo matching are demonstrated

Accelerating MR Imaging via Deep Chambolle-Pock Network

Compressed sensing (CS) has been introduced to accelerate data acquisition in MR Imaging. However, CS-MRI methods suffer from detail loss with large acceleration and complicated parameter selection. To address the limitations of existing CS-MRI methods, a model-driven MR reconstruction is proposed that trains a deep network, named CP-net, which is derived from the Chambolle-Pock algorithm to reconstruct the in vivo MR images of human brains from highly undersampled complex k-space data acquired on different types of MR scanners. The proposed deep network can learn the proximal operator and parameters among the Chambolle-Pock algorithm. All of the experiments show that the proposed CP-net achieves more accurate MR reconstruction results, outperforming state-of-the-art methods across various quantitative metrics.Comment: 4 pages, 5 figures, 1 table, Accepted at 2019 IEEE 41st Engineering in Medicine and Biology Conference (EMBC 2019

Deep Convolutional Framelets: A General Deep Learning Framework for Inverse Problems

Recently, deep learning approaches with various network architectures have achieved significant performance improvement over existing iterative reconstruction methods in various imaging problems. However, it is still unclear why these deep learning architectures work for specific inverse problems. To address these issues, here we show that the long-searched-for missing link is the convolution framelets for representing a signal by convolving local and non-local bases. The convolution framelets was originally developed to generalize the theory of low-rank Hankel matrix approaches for inverse problems, and this paper further extends the idea so that we can obtain a deep neural network using multilayer convolution framelets with perfect reconstruction (PR) under rectilinear linear unit nonlinearity (ReLU). Our analysis also shows that the popular deep network components such as residual block, redundant filter channels, and concatenated ReLU (CReLU) do indeed help to achieve the PR, while the pooling and unpooling layers should be augmented with high-pass branches to meet the PR condition. Moreover, by changing the number of filter channels and bias, we can control the shrinkage behaviors of the neural network. This discovery leads us to propose a novel theory for deep convolutional framelets neural network. Using numerical experiments with various inverse problems, we demonstrated that our deep convolution framelets network shows consistent improvement over existing deep architectures.This discovery suggests that the success of deep learning is not from a magical power of a black-box, but rather comes from the power of a novel signal representation using non-local basis combined with data-driven local basis, which is indeed a natural extension of classical signal processing theory.Comment: This will appear in SIAM Journal on Imaging Science