Monte Carlo SURE‐based parameter selection for parallel magnetic resonance imaging reconstruction

Purpose Regularizing parallel magnetic resonance imaging (MRI) reconstruction significantly improves image quality but requires tuning parameter selection. We propose a Monte Carlo method for automatic parameter selection based on Stein's unbiased risk estimate that minimizes the multichannel k‐space mean squared error (MSE). We automatically tune parameters for image reconstruction methods that preserve the undersampled acquired data, which cannot be accomplished using existing techniques. Theory We derive a weighted MSE criterion appropriate for data‐preserving regularized parallel imaging reconstruction and the corresponding weighted Stein's unbiased risk estimate. We describe a Monte Carlo approximation of the weighted Stein's unbiased risk estimate that uses two evaluations of the reconstruction method per candidate parameter value. Methods We reconstruct images using the denoising sparse images from GRAPPA using the nullspace method (DESIGN) and L 1 iterative self‐consistent parallel imaging (L 1 ‐SPIRiT). We validate Monte Carlo Stein's unbiased risk estimate against the weighted MSE. We select the regularization parameter using these methods for various noise levels and undersampling factors and compare the results to those using MSE‐optimal parameters. Results Our method selects nearly MSE‐optimal regularization parameters for both DESIGN and L 1 ‐SPIRiT over a range of noise levels and undersampling factors. Conclusion The proposed method automatically provides nearly MSE‐optimal choices of regularization parameters for data‐preserving nonlinear parallel MRI reconstruction methods. Magn Reson Med 71:1760–1770, 2014. © 2013 Wiley Periodicals, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106872/1/mrm24840.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/106872/2/mrm24840-sup-0001-suppinfo.pd

Superresolution imaging: A survey of current techniques

Cristóbal, G., Gil, E., Šroubek, F., Flusser, J., Miravet, C., Rodríguez, F. B., “Superresolution imaging: A survey of current techniques”, Proceedings of SPIE - The International Society for Optical Engineering, 7074, 2008. Copyright 2008. Society of Photo Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.Imaging plays a key role in many diverse areas of application, such as astronomy, remote sensing, microscopy, and tomography. Owing to imperfections of measuring devices (e.g., optical degradations, limited size of sensors) and instability of the observed scene (e.g., object motion, media turbulence), acquired images can be indistinct, noisy, and may exhibit insufficient spatial and temporal resolution. In particular, several external effects blur images. Techniques for recovering the original image include blind deconvolution (to remove blur) and superresolution (SR). The stability of these methods depends on having more than one image of the same frame. Differences between images are necessary to provide new information, but they can be almost unperceivable. State-of-the-art SR techniques achieve remarkable results in resolution enhancement by estimating the subpixel shifts between images, but they lack any apparatus for calculating the blurs. In this paper, after introducing a review of current SR techniques we describe two recently developed SR methods by the authors. First, we introduce a variational method that minimizes a regularized energy function with respect to the high resolution image and blurs. In this way we establish a unifying way to simultaneously estimate the blurs and the high resolution image. By estimating blurs we automatically estimate shifts with subpixel accuracy, which is inherent for good SR performance. Second, an innovative learning-based algorithm using a neural architecture for SR is described. Comparative experiments on real data illustrate the robustness and utilization of both methods.This research has been partially supported by the following grants: TEC2007-67025/TCM, TEC2006-28009-E, BFI-2003-07276, TIN-2004-04363-C03-03 by the Spanish Ministry of Science and Innovation, and by PROFIT projects FIT-070000-2003-475 and FIT-330100-2004-91. Also, this work has been partially supported by the Czech Ministry of Education under the project No. 1M0572 (Research Center DAR) and by the Czech Science Foundation under the project No. GACR 102/08/1593 and the CSIC-CAS bilateral project 2006CZ002

A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the non-local variations, jointly for the different components, through various $\ell_{1,p}$ matrix norms with $p \ge 1$. To facilitate the choice of the hyper-parameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for multispectral and hyperspectral images. The results demonstrate the interest of introducing a non-local structure tensor regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods

Simple and fast gradient-based impedance inversion using total variation regularization

We present an algorithm to estimate blocky images of the subsurface acoustic impedance (AI) from poststack seismic data. We regularize the resulting inverse problem, which is inherently ill-posed and non-unique, by means of the total variation semi-norm (TV). This allows us promote stable and blocky solutions which are, by virtue of the capability of TV to handle edges properly, adequate to model layered earth models with sharp contrasts. The use of the TV leads to a convex objective function easily minimized using a gradient-based algorithm that requires, in contrast to other AI inversion methods based on TV regularization, simple matrix-vector multiplications and no direct matrix inversion. The latter makes the algorithm numerically stable, easy to apply, and economic in terms of computational cost. Tests on synthetic and field data show that the proposed method, contrarily to conventional l2- or l1-norm regularized solutions, is able to provide blocky AI images that preserve the subsurface layered structure with good lateral continuity from noisy observations.Facultad de Ciencias Astronómicas y Geofísica

A SURE Approach for Digital Signal/Image Deconvolution Problems

In this paper, we are interested in the classical problem of restoring data degraded by a convolution and the addition of a white Gaussian noise. The originality of the proposed approach is two-fold. Firstly, we formulate the restoration problem as a nonlinear estimation problem leading to the minimization of a criterion derived from Stein's unbiased quadratic risk estimate. Secondly, the deconvolution procedure is performed using any analysis and synthesis frames that can be overcomplete or not. New theoretical results concerning the calculation of the variance of the Stein's risk estimate are also provided in this work. Simulations carried out on natural images show the good performance of our method w.r.t. conventional wavelet-based restoration methods