Compressed Sensing With Prior Information: Strategies, Geometry, and Bounds

We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via 1-1 and 1-2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruct the original signal. Our bounds and geometrical interpretations reveal that if the prior information has good enough quality, 1-1 minimization improves the performance of CS dramatically. In contrast, 1-2 minimization has a performance very similar to classical CS, and brings no significant benefits. In addition, we use the insight provided by our bounds to design practical schemes to improve prior information. All our findings are illustrated with experimental results

Data aggregation and recovery for the Internet of Things: A compressive demixing approach

Large-scale wireless sensor networks (WSNs) and Internet-of-Things (IoT) applications involve diverse sensing devices collecting and transmitting massive amounts of heterogeneous data. In this paper, we propose a novel compressive data aggregation and recovery mechanism that reduces the global communication cost without introducing computational overhead at the network nodes. Following the principles of compressive demixing, each node of the network collects measurement readings from multiple sources and mixes them with readings from other nodes into a single low-dimensional measurement vector, which is then relayed to other nodes; the constituent signals are recovered at the sink using convex optimization. Our design achieves significant reduction in the overall network data rates compared to prior schemes based on (distributed) compressed sensing or compressed sensing with (multiple) side information. Experiments using real large-scale air-quality data demonstrate the superior performance of the proposed framework against state-of-the-art solutions, with and without the presence of measurement and transmission noise

Coupled Dictionary Learning for Multi-contrast MRI Reconstruction

Magnetic resonance (MR) imaging tasks often involve multiple contrasts, such as T1-weighted, T2-weighted and Fluid-attenuated inversion recovery (FLAIR) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities in either structure level or gray level. In this paper, we propose a Coupled Dictionary Learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage the dependency correlation between different contrasts for guided or joint reconstruction from their under-sampled k-space data. Our approach iterates between three stages: coupled dictionary learning, coupled sparse denoising, and enforcing k-space consistency. The first stage learns a set of dictionaries that not only are adaptive to the contrasts, but also capture correlations among multiple contrasts in a sparse transform domain. By capitalizing on the learned dictionaries, the second stage performs coupled sparse coding to remove the aliasing and noise in the corrupted contrasts. The third stage enforces consistency between the denoised contrasts and the measurements in the k-space domain. Numerical experiments, consisting of retrospective under-sampling of various MRI contrasts with a variety of sampling schemes, demonstrate that CDLMRI is capable of capturing structural dependencies between different contrasts. The learned priors indicate notable advantages in multi-contrast MR imaging and promising applications in quantitative MR imaging such as MR fingerprinting

Coupled Dictionary Learning for Multi-contrast MRI Reconstruction

Medical imaging tasks often involve multiple contrasts, such as T1-and T2-weighted magnetic resonance imaging (MRI) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities. In this paper, we propose a Coupled Dictionary Learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage an available guidance contrast to restore the target contrast. Our approach consists of three stages: coupled dictionary learning, coupled sparse denoising, and k-space consistency enforcing. The first stage learns a group of dictionaries that capture correlations among multiple contrasts. By capitalizing on the learned adaptive dictionaries, the second stage performs joint sparse coding to denoise the corrupted target image with the aid of a guidance contrast. The third stage enforces consistency between the denoised image and the measurements in the k-space domain. Numerical experiments on the retrospective under-sampling of clinical MR images demonstrate that incorporating additional guidance contrast via our design improves MRI reconstruction, compared to state-of-the-art approaches

Multimodal image super-resolution via joint sparse representations induced by coupled dictionaries

Real-world data processing problems often involve various image modalities associated with a certain scene, including RGB images, infrared images, or multispectral images. The fact that different image modalities often share certain attributes, such as edges, textures, and other structure primitives, represents an opportunity to enhance various image processing tasks. This paper proposes a new approach to construct a high-resolution (HR) version of a low-resolution (LR) image, given another HR image modality as guidance, based on joint sparse representations induced by coupled dictionaries. The proposed approach captures complex dependency correlations, including similarities and disparities, between different image modalities in a learned sparse feature domain in lieu of the original image domain. It consists of two phases: coupled dictionary learning phase and coupled superresolution phase. The learning phase learns a set of dictionaries from the training dataset to couple different image modalities together in the sparse feature domain. In turn, the super-resolution phase leverages such dictionaries to construct an HR version of the LR target image with another related image modality for guidance. In the advanced version of our approach, multistage strategy and neighbourhood regression concept are introduced to further improve the model capacity and performance. Extensive guided image super-resolution experiments on real multimodal images demonstrate that the proposed approach admits distinctive advantages with respect to the state-of-the-art approaches, for example, overcoming the texture copying artifacts commonly resulting from inconsistency between the guidance and target images. Of particular relevance, the proposed model demonstrates much better robustness than competing deep models in a range of noisy scenarios

Coupled dictionary learning for multi-contrast MRI reconstruction

Magnetic resonance (MR) imaging tasks often involve multiple contrasts, such as T1-weighted, T2-weighted and Fluid-attenuated inversion recovery (FLAIR) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities in either structure level or gray level. In this paper, we propose a Coupled Dictionary Learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage the dependency correlation between different contrasts for guided or joint reconstruction from their under-sampled k-space data. Our approach iterates between three stages: coupled dictionary learning, coupled sparse denoising, and enforcing k-space consistency. The first stage learns a set of dictionaries that not only are adaptive to the contrasts, but also capture correlations among multiple contrasts in a sparse transform domain. By capitalizing on the learned dictionaries, the second stage performs coupled sparse coding to remove the aliasing and noise in the corrupted contrasts. The third stage enforces consistency between the denoised contrasts and the measurements in the k-space domain. Numerical experiments, consisting of retrospective under-sampling of various MRI contrasts with a variety of sampling schemes, demonstrate that CDLMRI is capable of capturing structural dependencies between different contrasts. The learned priors indicate notable advantages in multi-contrast MR imaging and promising applications in quantitative MR imaging such as MR fingerprinting