16 research outputs found
Simultaneous use of Individual and Joint Regularization Terms in Compressive Sensing: Joint Reconstruction of Multi-Channel Multi-Contrast MRI Acquisitions
Purpose: A time-efficient strategy to acquire high-quality multi-contrast
images is to reconstruct undersampled data with joint regularization terms that
leverage common information across contrasts. However, these terms can cause
leakage of uncommon features among contrasts, compromising diagnostic utility.
The goal of this study is to develop a compressive sensing method for
multi-channel multi-contrast magnetic resonance imaging (MRI) that optimally
utilizes shared information while preventing feature leakage.
Theory: Joint regularization terms group sparsity and colour total variation
are used to exploit common features across images while individual sparsity and
total variation are also used to prevent leakage of distinct features across
contrasts. The multi-channel multi-contrast reconstruction problem is solved
via a fast algorithm based on Alternating Direction Method of Multipliers.
Methods: The proposed method is compared against using only individual and
only joint regularization terms in reconstruction. Comparisons were performed
on single-channel simulated and multi-channel in-vivo datasets in terms of
reconstruction quality and neuroradiologist reader scores.
Results: The proposed method demonstrates rapid convergence and improved
image quality for both simulated and in-vivo datasets. Furthermore, while
reconstructions that solely use joint regularization terms are prone to
leakage-of-features, the proposed method reliably avoids leakage via
simultaneous use of joint and individual terms.
Conclusion: The proposed compressive sensing method performs fast
reconstruction of multi-channel multi-contrast MRI data with improved image
quality. It offers reliability against feature leakage in joint
reconstructions, thereby holding great promise for clinical use.Comment: 13 pages, 13 figures. Submitted for possible publicatio
The block mutual coherence property condition for signal recovery
Compressed sensing shows that a sparse signal can stably be recovered from
incomplete linear measurements. But, in practical applications, some signals
have additional structure, where the nonzero elements arise in some blocks. We
call such signals as block-sparse signals. In this paper, the
minimization method for the stable recovery of
block-sparse signals is investigated. Sufficient conditions based on block
mutual coherence property and associating upper bound estimations of error are
established to ensure that block-sparse signals can be stably recovered in the
presence of noise via the minimization method. For
all we know, it is the first block mutual coherence property condition of
stably reconstructing block-sparse signals by the
minimization method. Additionally, the numerical experiments implemented verify
the performance of the minimization.Comment: 14 pages, 8 figure
Architecture for one-shot compressive imaging using computer-generated holograms.
We propose a synchronous implementation of compressive imaging. This method is mathematically equivalent to prevailing sequential methods, but uses a static holographic optical element to create a spatially distributed spot array from which the image can be reconstructed with an instantaneous measurement. We present the holographic design requirements and demonstrate experimentally that the linear algebra of compressed imaging can be implemented with this technique. We believe this technique can be integrated with optical metasurfaces, which will allow the development of new compressive sensing methods.Engineering and Physical Sciences Research Council (EPSRC) (EP/G037256/1, EP/L015455/1)