Sparsifying Transform Research Articles

Accelerated parallel magnetic resonance imaging with compressed sensing using structured sparsity.

We present a method that combines compressed sensing with parallel imaging that takes advantage of the structure of the sparsifying transformation. Previous work has combined compressed sensing with parallel imaging using model-based reconstruction but without taking advantage of the structured sparsity. Blurry images for each coil are reconstructed from the fully sampled center region. The optimization problem of compressed sensing is modified to take these blurry images into account, and it is solved to estimate the missing details. Using data of brain, ankle, and shoulder anatomies, the combination of compressed sensing with structured sparsity and parallel imaging reconstructs an image with a lower relative error than does sparse SENSE or L1 ESPIRiT, which do not use structured sparsity. Taking advantage of structured sparsity improves the image quality for a given amount of data as long as a fully sampled region centered on the zero frequency of the appropriate size is acquired.

The Experimental Method of Sparse Measurement Based on Target’s Radar Cross Section Data

In experiments of testing targets’ radar cross section (RCS), RCS is a measure of the target’s ability to reflect radar signals in the direction of radar reception. In order to take non blurry spatial-domain imaging of the target, sampling or measuring the target’s RCS signal must meet the Nyquist sampling theorem. However, RCS testing in microwave darkroom would produce a significant amount of sampling data, which requires a very long testing period. Based on the sparsity of spatial-domain RCS data after sparsifying transformation, a sparse projection measurement experimental method is designed for frequency-domain RCS data by sparsely sampling frequency-domain signals, fully utilizing the correlation between row and column information of two-dimensional frequency-domain data and the global sparsity of two-dimensional spatial-domain data. Finally, based on sparsely sampled data in the frequency-domain, the original RCS data is reconstructed by reconstruction algorithms, achieving the goal of effectively reducing RCS sampling data in RCS testing experiments.

PRIMIS: Privacy-preserving medical image sharing via deep sparsifying transform learning with obfuscation

Objective:The primary objective of our study is to address the challenge of confidentially sharing medical images across different centers. This is often a critical necessity in both clinical and research environments, yet restrictions typically exist due to privacy concerns. Our aim is to design a privacy-preserving data-sharing mechanism that allows medical images to be stored as encoded and obfuscated representations in the public domain without revealing any useful or recoverable content from the images. In tandem, we aim to provide authorized users with compact private keys that could be used to reconstruct the corresponding images. Method:Our approach involves utilizing a neural auto-encoder. The convolutional filter outputs are passed through sparsifying transformations to produce multiple compact codes. Each code is responsible for reconstructing different attributes of the image. The key privacy-preserving element in this process is obfuscation through the use of specific pseudo-random noise. When applied to the codes, it becomes computationally infeasible for an attacker to guess the correct representation for all the codes, thereby preserving the privacy of the images. Results:The proposed framework was implemented and evaluated using chest X-ray images for different medical image analysis tasks, including classification, segmentation, and texture analysis. Additionally, we thoroughly assessed the robustness of our method against various attacks using both supervised and unsupervised algorithms. Conclusion:This study provides a novel, optimized, and privacy-assured data-sharing mechanism for medical images, enabling multi-party sharing in a secure manner. While we have demonstrated its effectiveness with chest X-ray images, the mechanism can be utilized in other medical images modalities as well.

Group Membership Verification via Nonlinear Sparsifying Transform Learning

Group Membership Verification via Nonlinear Sparsifying Transform Learning

Fast Parallel Magnetic Resonance Imaging Reconstruction Based on Sparsifying Transform Learning and Structured Low-Rank Model

Fast Parallel Magnetic Resonance Imaging Reconstruction Based on Sparsifying Transform Learning and Structured Low-Rank Model

Multi-layer clustering-based residual sparsifying transform for low-dose CT image reconstruction.

The recently proposed sparsifying transform (ST) models incur low computational cost and have been applied to medical imaging. Meanwhile, deep models with nested network structure reveal great potential for learning features in different layers. In this study, we propose a network-structured ST learning approach for X-ray computed tomography (CT), which we refer to as multi-layer clustering-based residual sparsifying transform (MCST) learning. The proposed MCST scheme learns multiple different unitary transforms in each layer by dividing each layer's input into several classes. We apply the MCST model to low-dose CT (LDCT) reconstruction by deploying the learned MCST model into the regularizer in penalized weighted least squares (PWLS) reconstruction. The proposed MCST model combines a multi-layer sparse representation structure with multiple clusters for the features in each layer that are modeled by a rich collection of transforms. We train the MCST model in an unsupervised manner via a block coordinate descent (BCD) algorithm. Since our method is patch-based, the training can be performed with a limited set of images. For CT image reconstruction, we devise a novel algorithm called PWLS-MCST by integrating the pre-learned MCST signal model with PWLSoptimization. We conducted LDCT reconstruction experiments on XCAT phantom data, Numerical Mayo Clinical CT dataset and "LDCT image and projection dataset" (Clinical LDCT dataset). We trained the MCST model with two (or three) layers and with five clusters in each layer. The learned transforms in the same layer showed rich features while additional information is extracted from representation residuals. Our simulation results and clinical results demonstrate that PWLS-MCST achieves better image reconstruction quality than the conventional filtered back-projection (FBP) method and PWLS with edge-preserving (EP) regularizer. It also outperformed recent advanced methods like PWLS with a learned multi-layer residual sparsifying transform (MARS) prior and PWLS with a union of learned transforms (ULTRA), especially for displaying clear edges and preserving subtledetails. In this work, a multi-layer sparse signal model with a nested network structure is proposed. We refer this novel model as the MCST model that exploits multi-layer residual maps to sparsify the underlying image and clusters the inputs in each layer for accurate sparsification. We presented a new PWLS framework with a learned MCST regularizer for LDCT reconstruction. Experimental results show that the proposed PWLS-MCST provides clearer reconstructions than several baseline methods. The code for PWLS-MCST is released at https://github.com/Xikai97/PWLS-MCST.

Utilizing the structure of a redundant dictionary comprised of wavelets and curvelets with compressed sensing

The discrete curvelet transform decomposes an image into a set of fundamental components that are distinguished by direction and size as well as a low-frequency representation. The curvelet representation is approximately sparse; thus, it is a useful sparsifying transformation to be used with compressed sensing. However, the low-frequency portion is seldom sparse. This manuscript presents a method to modify the redundant sparsifying transformation comprised of the wavelet and curvelet transforms to take advantage of this fact with compressed sensing image reconstruction. Instead of relying on sparsity for this low-frequency estimate, the Nyquist-Shannon theorem specifies a square region centered on the $0$ frequency to be collected, which is used to generate a blurry estimate. A Basis Pursuit Denoising problem is solved to determine the missing details after modifying the sparsifying transformation to take advantage of the known fully sampled region. Improvements in quality are shown on magnetic resonance and optical images.

Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data.

The discrete shearlet transformation accurately represents the discontinuities and edges occurring in magnetic resonance imaging, providing an excellent option of a sparsifying transform. In the present paper, we examine the use of discrete shearlets over other sparsifying transforms in a low-rank plus sparse decomposition problem, denoted by . The proposed algorithm is evaluated on simulated dynamic contrast enhanced (DCE) and small bowel data. For the small bowel, eight subjects were scanned; the sequence was run first on breath-holding and subsequently on free-breathing, without changing the anatomical position of the subject. The reconstruction performance of the proposed algorithm was evaluated against k-t FOCUSS. decomposition, using discrete shearlets as sparsifying transforms, successfully separated the low-rank (background and periodic motion) from the sparse component (enhancement or bowel motility) for both DCE and small bowel data. Motion estimated from low-rank of DCE data is closer to ground truth deformations than motion estimated from L and S. Motility metrics derived from the S component of free-breathing data were not significantly different from the ones from breath-holding data up to four-fold undersampling, indicating that bowel (rapid/random) motility is isolated in S. Our work strongly supports the use of discrete shearlets as a sparsifying transform in a decomposition for undersampled MR data.

Noise reduction in diffusion weighted MRI of the pancreas using an L1-regularized iterative SENSE reconstruction

ObjectivesTo prospectively evaluate an L1 regularized iterative SENSE reconstruction (L1-R SENSE) to eliminate band-like artifacts frequently seen with parallel imaging (SENSE) at high acceleration factors in high resolution diffusion weighted magnetic resonance imaging of the pancreas. MethodsFourteen patients with pancreatic ductal adenocarcinoma (PDAC) underwent respiratory triggered DWI ss-EPI at a resolution of 2.5 × 2.5 × 3 mm3 with uniform undersampling in the phase encoding direction (AP axis) with an acceleration factor of 4. Data were reconstructed using the standard SENSE reconstruction routine of the vendor and an iterative SENSE reconstruction employing L1 regularization after a wavelet sparsifying transformation (L1-R SENSE). Retrospective reconstruction of the data with a lower number of averages was performed using both reconstruction methods. Two radiologists independently assessed noise artifacts, anatomical details and image quality (IQ) subjectively with a 4-point scale. Apparent diffusion coefficient (ADC) and covariance (CV) of ADC estimated from images reconstructed at a different number of averages for PDAC and the normal pancreas were assessed. ResultsL1-R SENSE resulted in higher IQ and less noise artifacts than SENSE. Anatomical details were significantly higher for SENSE in one reader. Mean ADC of PDAC and normal pancreas were significantly higher for L1-R SENSE than SENSE. L1-R SENSE revealed lower CV of ADC for normal pancreas compared to SENSE, whereas no difference was noted for PDAC. ConclusionCompared with traditional SENSE reconstruction, L1-R SENSE effectively reduces band-like noise and improves the robustness of the ADC estimation from acquisitions using single-shot DW-EPI of the pancreas.

An Improved Image Filtering Algorithm for Mixed Noise

In recent years, image filtering has been a hot research direction in the field of image processing. Experts and scholars have proposed many methods for noise removal in images, and these methods have achieved quite good denoising results. However, most methods are performed on single noise, such as Gaussian noise, salt and pepper noise, multiplicative noise, and so on. For mixed noise removal, such as salt and pepper noise + Gaussian noise, although some methods are currently available, the denoising effect is not ideal, and there are still many places worthy of improvement and promotion. To solve this problem, this paper proposes a filtering algorithm for mixed noise with salt and pepper + Gaussian noise that combines an improved median filtering algorithm, an improved wavelet threshold denoising algorithm and an improved Non-local Means (NLM) algorithm. The algorithm makes full use of the advantages of the median filter in removing salt and pepper noise and demonstrates the good performance of the wavelet threshold denoising algorithm and NLM algorithm in filtering Gaussian noise. At first, we made improvements to the three algorithms individually, and then combined them according to a certain process to obtain a new method for removing mixed noise. Specifically, we adjusted the size of window of the median filtering algorithm and improved the method of detecting noise points. We improved the threshold function of the wavelet threshold algorithm, analyzed its relevant mathematical characteristics, and finally gave an adaptive threshold. For the NLM algorithm, we improved its Euclidean distance function and the corresponding distance weight function. In order to test the denoising effect of this method, salt and pepper + Gaussian noise with different noise levels were added to the test images, and several state-of-the-art denoising algorithms were selected to compare with our algorithm, including K-Singular Value Decomposition (KSVD), Non-locally Centralized Sparse Representation (NCSR), Structured Overcomplete Sparsifying Transform Model with Block Cosparsity (OCTOBOS), Trilateral Weighted Sparse Coding (TWSC), Block Matching and 3D Filtering (BM3D), and Weighted Nuclear Norm Minimization (WNNM). Experimental results show that our proposed algorithm is about 2–7 dB higher than the above algorithms in Peak Signal-Noise Ratio (PSNR), and also has better performance in Root Mean Square Error (RMSE), Structural Similarity (SSIM), and Feature Similarity (FSIM). In general, our algorithm has better denoising performance, better restoration of image details and edge information, and stronger robustness than the above-mentioned algorithms.

Utilizing the Wavelet Transform's Structure in Compressed Sensing.

Compressed sensing has empowered quality image reconstruction with fewer data samples than previously thought possible. These techniques rely on a sparsifying linear transformation. The Daubechies wavelet transform is commonly used for this purpose. In this work, we take advantage of the structure of this wavelet transform and identify an affine transformation that increases the sparsity of the result. After inclusion of this affine transformation, we modify the resulting optimization problem to comply with the form of the Basis Pursuit Denoising problem. Finally, we show theoretically that this yields a lower bound on the error of the reconstruction and present results where solving this modified problem yields images of higher quality for the same sampling patterns using both magnetic resonance and optical images.

Low‐Rank Combined Adaptive Sparsifying Transform for Blind Compressed Sensing Image Recovery

Compressed sensing (CS) exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undegraded images. Because the synthesis dictionary learning methods involves NP-hard sparse coding and expensive learning steps, sparsifying transform based blind compressed sending (BCS) has been shown to be effective and efficient in applications, while also enjoying good convergence guarantees. By minimizing the rank of an overlapped patch group matrix to efficiently exploit the nonlocal self-similarity features of the image, while the sparsifying transform model imposes the local features of the image. We propose a combined low-rank and adaptive sparsifying transform (LRAST) BCS method to better represent natural images. We utilized the patch coordinate (PCD) descent algorithm to optimize the method, and this enforced the intrinsic local sparsity and nonlocal self-similarity of the images simultaneously in a unified framework. The experimental results indicated a promising performance, even in comparison to state-of-theart methods.

Cross-Scale Predictive Dictionaries.

Sparse representations using data dictionaries provide an efficient model particularly for signals that do not enjoy alternate analytic sparsifying transformations. However, solving inverse problems with sparsifying dictionaries can be computationally expensive, especially when the dictionary under consideration has a large number of atoms. In this paper, we incorporate additional structure on to dictionary-based sparse representations for visual signals to enable speedups when solving sparse approximation problems. The specific structure that we endow onto sparse models is that of a multi-scale modeling where the sparse representation at each scale is constrained by the sparse representation at coarser scales. We show that this cross-scale predictive model delivers significant speedups, often in the range of , with little loss in accuracy for linear inverse problems associated with images, videos, and light fields.

Graph Topology Inference Based on Sparsifying Transform Learning

Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse representation of the graph signal leading to a modular graph whose Laplacian matrix admits the found dictionary as its eigenvectors. The role of sparsity here is to induce a band-limited representation or, equivalently, a modular structure of the graph. The proposed strategy is composed of two optimization steps: i) learning an orthonormal sparsifying transform from the data; ii) recovering the Laplacian, and then topology, from the transform. The first step is achieved through an iterative algorithm whose alternating intermediate solutions are expressed in closed form. The second step recovers the Laplacian matrix from the sparsifying transform through a convex optimization method. Numerical results corroborate the effectiveness of the proposed methods over both synthetic data and real brain data, used for inferring the brain functionality network through experiments conducted over patients affected by epilepsy.

Joint learning sparsifying linear transformation for low-resolution image synthesis and recognition

Many computer vision problems involve exploring the synthesis and classification models that map images from the observed source space to a target space. Recently, one popular and effective method is to transform images from both source and target space into a shared single sparse domain, in which a synthesis model is established. Motivated by such a technique, this research attempts to explore an effective and robust linear function that maps the sparse representatio ns of images from the source space to the target space, and simultaneously develop a linear classifier on such a coupled space with both supervised and semi-supervised learning. In order to capture the sparse structure shared by each class, we represent this mapping using a linear transformation with the constraint of sparsity. The performance of our proposed method is evaluated on several benchmark image datasets for low-resolution faces/digits classification and super-resolution, and the experimental results verify the effectiveness of the proposed method.

Accelerated Algorithm for Compressed Sensing Using Nonlinear Sparsifying Transform in CT Image Reconstruction

Accelerated Algorithm for Compressed Sensing Using Nonlinear Sparsifying Transform in CT Image Reconstruction

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.

Combined Similarity to Reference Image with Joint Sparsifying Transform for Longitudinal Compressive Sensing MRI

It is challenging to save acquisition time and reconstruct a medical magnetic resonance (MR) image with important details and features from its compressive measurements. In this paper, a novel method is proposed for longitudinal compressive sensing (LCS) MR imaging (MRI), where the similarity between reference and acquired image is combined with joint sparsifying transform. Furthermore, the joint sparsifying transform with the wavelet and the Contourlet can efficiently represent both isotropic and anisotropic features and the objective function is solved by extended smooth-based monotone version of the fast iterative shrinkage thresholding algorithm (SFISTA). The experiment results demonstrate that the existing regularization model obtains better performance with less acquisition time and recovers both edges and fine details of MR images, much better than the existing regularization model based on the similarity and the wavelet transform for LCS-MRI.

An Efficient Algorithm for Overcomplete Sparsifying Transform Learning with Signal Denoising

This paper deals with the problem of overcomplete transform learning. An alternating minimization based procedure is proposed for solving the formulated sparsifying transform learning problem. A closed-form solution is derived for the minimization involved in transform update stage. Compared with existing ones, our proposed algorithm significantly reduces the computation complexity. Experiments and simulations are carried out with synthetic data and real images to demonstrate the superiority of the proposed approach in terms of the averaged representation and denoising errors, the percentage of successful and meaningful recovery of the analysis dictionary, and, more significantly, the computation efficiency.

Proposal of Compressed Sensing Using Nonlinear Sparsifying Transform for CT Image Reconstruction

Proposal of Compressed Sensing Using Nonlinear Sparsifying Transform for CT Image Reconstruction