Compressive sensing based image processing and energy-efficient hardware implementation with application to MRI and JPG 2000

In the present age of technology, the buzzwords are low-power, energy-efficient and compact systems. This directly leads to the date processing and hardware techniques employed in the core of these devices. One of the most power-hungry and space-consuming schemes is that of image/video processing, due to its high quality requirements. In current design methodologies, a point has nearly been reached in which physical and physiological effects limit the ability to just encode data faster. These limits have led to research into methods to reduce the amount of acquired data without degrading image quality and increasing the energy consumption. Compressive sensing (CS) has emerged as an efficient signal compression and recovery technique, which can be used to efficiently reduce the data acquisition and processing. It exploits the sparsity of a signal in a transform domain to perform sampling and stable recovery. This is an alternative paradigm to conventional data processing and is robust in nature. Unlike the conventional methods, CS provides an information capturing paradigm with both sampling and compression. It permits signals to be sampled below the Nyquist rate, and still allowing optimal reconstruction of the signal. The required measurements are far less than those of conventional methods, and the process is non-adaptive, making the sampling process faster and universal. In this thesis, CS methods are applied to magnetic resonance imaging (MRI) and JPEG 2000, which are popularly used imaging techniques in clinical applications and image compression, respectively. Over the years, MRI has improved dramatically in both imaging quality and speed. This has further revolutionized the field of diagnostic medicine. However, imaging speed, which is essential to many MRI applications still remains a major challenge. The specific challenge addressed in this work is the use of non-Fourier based complex measurement-based data acquisition. This method provides the possibility of reconstructing high quality MRI data with minimal measurements, due to the high incoherence between the two chosen matrices. Similarly, JPEG2000, though providing a high compression, can be further improved upon by using compressive sampling. In addition, the image quality is also improved. Moreover, having a optimized JPEG 2000 architecture reduces the overall processing, and a faster computation when combined with CS. Considering the requirements, this thesis is presented in two parts. In the first part: (1) A complex Hadamard matrix (CHM) based 2D and 3D MRI data acquisition with recovery using a greedy algorithm is proposed. The CHM measurement matrix is shown to satisfy the necessary condition for CS, known as restricted isometry property (RIP). The sparse recovery is done using compressive sampling matching pursuit (CoSaMP); (2) An optimized matrix and modified CoSaMP is presented, which enhances the MRI performance when compared with the conventional sampling; (3) An energy-efficient, cost-efficient hardware design based on field programmable gate array (FPGA) is proposed, to provide a platform for low-cost MRI processing hardware. At every stage, the design is proven to be superior with other commonly used MRI-CS methods and is comparable with the conventional MRI sampling. In the second part, CS techniques are applied to image processing and is combined with JPEG 2000 coder. While CS can reduce the encoding time, the effect on the overall JPEG 2000 encoder is not very significant due to some complex JPEG 2000 algorithms. One problem encountered is the big-level operations in JPEG 2000 arithmetic encoding (AE), which is completely based on bit-level operations. In this work, this problem is tackled by proposing a two-symbol AE with an efficient FPGA based hardware design. Furthermore, this design is energy-efficient, fast and has lower complexity when compared to conventional JPEG 2000 encoding

Investigation of Sparsifying Transforms in Compressed Sensing for Magnetic Resonance Imaging with Fasttestcs

The goal of this contribution is to achieve higher reduction factors for faster Magnetic Resonance Imaging (MRI) scans with better Image Quality (IQ) by using Compressed Sensing (CS). This can be accomplished by adopting and understanding better sparsifying transforms for CS in MRI. There is a tremendous number of transforms and optional settings potentially available. Additionally, the amount of research in CS is growing, with possible duplication and difficult practical evaluation and comparison. However, no in-depth analysis of the effectiveness of different redundant sparsifying transforms on MRI images with CS has been undertaken until this work. New theoretical sparsity bounds for the dictionary restricted isometry property constants in CS are presented with mathematical proof. In order to verify the sparsifying transforms in this setting, the experiments focus on several redundant transforms contrasting them with orthogonal transforms. The transforms investigated are Wavelet (WT), Cosine (CT), contourlet, curvelet, k-means singular value decomposition, and Gabor. Several variations of these transforms with corresponding filter options are developed and tested in compression and CS simulations. Translation Invariance (TI) in transforms is found to be a key contributing factor in producing good IQ because any particular translation of the signal will not effect the transform representation. Some transforms tested here are TI and many others are made TI by transforming small overlapping image patches. These transforms are tested by comparing different under-sampling patterns and reduction ratios with varying image types including MRI data. Radial, spiral, and various random patterns are implemented and demonstrate that the TIWT is very robust across all under-sampling patterns. Results of the TIWT simulations show improvements in de-noising and artifact suppression over that of individual orthogonal wavelets and total variation ell-1 minimization in CS simulations. Some of these transforms add considerable time to the CS simulations and prohibit extensive testing of large 3D MRI datasets. Therefore, the FastTestCS software simulation framework is developed and customized for testing images, under-samping patterns and sparsifying transforms. This novel software is offered as a practical, robust, universal framework for evaluating and developing simulations in order to quickly test sparsifying transforms for CS MRI

AliasNet: Alias Artefact Suppression Network for Accelerated Phase-Encode MRI

Sparse reconstruction is an important aspect of MRI, helping to reduce acquisition time and improve spatial-temporal resolution. Popular methods are based mostly on compressed sensing (CS), which relies on the random sampling of k-space to produce incoherent (noise-like) artefacts. Due to hardware constraints, 1D Cartesian phase-encode under-sampling schemes are popular for 2D CS-MRI. However, 1D under-sampling limits 2D incoherence between measurements, yielding structured aliasing artefacts (ghosts) that may be difficult to remove assuming a 2D sparsity model. Reconstruction algorithms typically deploy direction-insensitive 2D regularisation for these direction-associated artefacts. Recognising that phase-encode artefacts can be separated into contiguous 1D signals, we develop two decoupling techniques that enable explicit 1D regularisation and leverage the excellent 1D incoherence characteristics. We also derive a combined 1D + 2D reconstruction technique that takes advantage of spatial relationships within the image. Experiments conducted on retrospectively under-sampled brain and knee data demonstrate that combination of the proposed 1D AliasNet modules with existing 2D deep learned (DL) recovery techniques leads to an improvement in image quality. We also find AliasNet enables a superior scaling of performance compared to increasing the size of the original 2D network layers. AliasNet therefore improves the regularisation of aliasing artefacts arising from phase-encode under-sampling, by tailoring the network architecture to account for their expected appearance. The proposed 1D + 2D approach is compatible with any existing 2D DL recovery technique deployed for this application

Fractal Compressive Sensing

This paper introduces a sparse projection matrix composed of discrete (digital) periodic lines that create a pseudo-random (p.frac) sampling scheme. Our approach enables random Cartesian sampling whilst employing deterministic and one-dimensional (1D) trajectories derived from the discrete Radon transform (DRT). Unlike radial trajectories, DRT projections can be back-projected without interpolation. Thus, we also propose a novel reconstruction method based on the exact projections of the DRT called finite Fourier reconstruction (FFR). We term this combined p.frac and FFR strategy, finite compressive sensing (FCS), with image recovery demonstrated on experimental and simulated data; image quality comparisons are made with Cartesian random sampling in 1D and two-dimensional (2D), as well as radial under-sampling in a more constrained experiment. Our experiments indicate FCS enables 3-5dB gain in peak signal-to-noise ratio (PSNR) for 2-, 4- and 8-fold under-sampling compared to 1D Cartesian random sampling. This paper aims to: Review common sampling strategies for compressed sensing (CS)-magnetic resonance imaging (MRI) to inform the motivation of a projective and Cartesian sampling scheme. Compare the incoherence of these sampling strategies and the proposed p.frac. Compare reconstruction quality of the sampling schemes under various reconstruction strategies to determine the suitability of p.frac for CS-MRI. It is hypothesised that because p.frac is a highly incoherent sampling scheme, that reconstructions will be of high quality compared to 1D Cartesian phase-encode under-sampling.Comment: 12 pages, 10 figures, 1 tabl

Advanced parallel magnetic resonance imaging methods with applications to MR spectroscopic imaging

Parallel magnetic resonance imaging offers a framework for acceleration of conventional MRI encoding using an array of receiver coils with spatially-varying sensitivities. Novel encoding and reconstruction techniques for parallel MRI are investigated in this dissertation. The main goal is to improve the actual reconstruction methods and to develop new approaches for massively parallel MRI systems that take advantage of the higher information content provided by the large number of small receivers. A generalized forward model and inverse reconstruction with regularization for parallel MRI with arbitrary k-space sub-sampling is developed. Regularization methods using the singular value decomposition of the encoding matrix and pre-conditioning of the forward model are proposed to desensitize the solution from data noise and model errors. Variable density k-space sub-sampling is presented to improve the reconstruction with the common uniform sub-sampling. A novel method for massively parallel MRI systems named Superresolution Sensitivity Encoding (SURE-SENSE) is proposed where acceleration is performed by acquiring the low spatial resolution representation of the object being imaged and the stronger sensitivity variation from small receiver coils is used to perform intra-pixel reconstruction. SURE-SENSE compares favorably the performance of standard SENSE reconstruction for low spatial resolution imaging such as spectroscopic imaging. The methods developed in this dissertation are applied to Proton Echo Planar Spectroscopic Imaging (PEPSI) for metabolic imaging in human brain with high spatial and spectral resolution in clinically feasible acquisition times. The contributions presented in this dissertation are expected to provide methods that substantially enhance the utility of parallel MRI for clinical research and to offer a framework for fast MRSI of human brain with high spatial and spectral resolution

Learning Sub-Sampling and Signal Recovery with Applications in Ultrasound Imaging

Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted considerable attention in recent years. Compressed sensing emerged as a popular framework for sparse signal reconstruction from a small set of compressed measurements. However, typical compressed sensing designs measure a (non)linearly weighted combination of all input signal elements, which poses practical challenges. These designs are also not necessarily task-optimal. In addition, real-time recovery is hampered by the iterative and time-consuming nature of sparse recovery algorithms. Recently, deep learning methods have shown promise for fast recovery from compressed measurements, but the design of adequate and practical sensing strategies remains a challenge. Here, we propose a deep learning solution termed Deep Probabilistic Sub-sampling (DPS), that learns a task-driven sub-sampling pattern, while jointly training a subsequent task model. Once learned, the task-based sub-sampling patterns are fixed and straightforwardly implementable, e.g. by non-uniform analog-to-digital conversion, sparse array design, or slow-time ultrasound pulsing schemes. The effectiveness of our framework is demonstrated in-silico for sparse signal recovery from partial Fourier measurements, and in-vivo for both anatomical image and tissue-motion (Doppler) reconstruction from sub-sampled medical ultrasound imaging data

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Image Reconstructions of Compressed Sensing MRI with Multichannel Data

Magnetic resonance imaging (MRI) provides high spatial resolution, high-quality of soft-tissue contrast, and multi-dimensional images. However, the speed of data acquisition limits potential applications. Compressed sensing (CS) theory allowing data being sampled at sub-Nyquist rate provides a possibility to accelerate the MRI scan time. Since most MRI scanners are currently equipped with multi-channel receiver systems, integrating CS with multi-channel systems can further shorten the scan time and also provide a better image quality. In this dissertation, we develop several techniques for integrating CS with parallel MRI. First, we propose a method which extends the reweighted l1 minimization to the CS-MRI with multi-channel data. The individual channel images are recovered according to the reweighted l1 minimization algorithm. Then, the final image is combined by the sum-of-squares method. Computer simulations show that the new method can improve the reconstruction quality at a slightly increased computation cost. Second, we propose a reconstruction approach using the ubiquitously available multi-core CPU to accelerate CS reconstructions of multiple channel data. CS reconstructions for phase array system using iterative l1 minimization are significantly time-consuming, where the computation complexity scales with the number of channels. The experimental results show that the reconstruction efficiency benefits significantly from parallelizing the CS reconstructions, and pipelining multi-channel data on multi-core processors. In our experiments, an additional speedup factor of 1.6 to 2.0 was achieved using the proposed method on a quad-core CPU. Finally, we present an efficient reconstruction method for high-dimensional CS MRI with a GPU platform to shorten the time of iterative computations. Data managements as well as the iterative algorithm are properly designed to meet the way of SIMD (single instruction/multiple data) parallelizations. For three-dimension multi-channel data, all slices along frequency encoding direction and multiple channels are highly parallelized and simultaneously processed within GPU. Generally, the runtime on GPU only requires 2.3 seconds for reconstructing a simulated 4-channel data with a volume size of 256×256×32. Comparing to 67 seconds using CPU, it achieves 28 faster with the proposed method. The rapid reconstruction algorithms demonstrated in this work are expected to help bring high dimensional, multichannel parallel CS MRI closer to clinical applications