### Nonlocal transform-domain denoising of volumetric data with groupwise adaptive variance estimation

"... We propose an extension of the BM4D volumetric filter to the denoising of data corrupted by spatially nonuniform noise. BM4D implements the grouping and collaborative filtering paradigm, where similar cubes of voxels are stacked into a four-dimensional “group”. Each group undergoes a sparsifying fou ..."

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We propose an extension of the BM4D volumetric filter to the denoising of data corrupted by spatially nonuniform noise. BM4D implements the grouping and collaborative filtering paradigm, where similar cubes of voxels are stacked into a four-dimensional “group”. Each group undergoes a sparsifying four-dimensional transform, that exploits the local correlation among voxels in each cube and the nonlocal correlation between corresponding voxels of different cubes. Thus, signal and noise are effectively separated in transform domain. In this work we take advantage of the sparsity induced by the four-dimensional transform to provide a spatially adaptive estimation of the local noise variance by applying a robust median estimator of the absolute deviation to the spectrum of each filtered group. The adaptive variance estimates are then used during coefficients shrinkage. Finally, the inverse four-dimensional transform is applied to the filtered group, and each individual cube estimate is adaptively aggregated at its original location. Experiments on medical data corrupted by spatially varying Gaussian and Rician noise demonstrate the efficacy of the proposed approach in volumetric data denoising. In case of magnetic resonance signals, the adaptive variance estimate can be also used to compensate the estimation bias due to the non-zero-mean errors of the Rician-distributed data.

### Author manuscript, published in "ISBI 2011, United States (2011)" IMAGE RECONSTRUCTION FROM MULTIPLE SENSORS USING STEIN’S PRINCIPLE. APPLICATION TO PARALLEL MRI.

, 2012

"... We are interested in image reconstruction when data provided by several sensors are corrupted with a linear operator and an additive white Gaussian noise. This problem is addressed by invoking Stein’s Unbiased Risk Estimate (SURE) techniques. The key advantage of SURE methods is that they do not req ..."

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We are interested in image reconstruction when data provided by several sensors are corrupted with a linear operator and an additive white Gaussian noise. This problem is addressed by invoking Stein’s Unbiased Risk Estimate (SURE) techniques. The key advantage of SURE methods is that they do not require prior knowledge about the statistics of the unknown image, while yielding an expression of the Mean Square Error (MSE) only depending on the statistics of the observed data. Hence, they avoid the difficult problem of hyperparameter estimation related to some prior distribution, which traditionally needs to be addressed in variational or Bayesian approaches. Consequently, a SURE approach can be applied by directly parameterizing a wavelet-based estimator and finding the optimal parameters that minimize the MSE estimate in reconstruction problems. Simulations carried out on parallel Magnetic Resonance Imaging (pMRI) images show the improved performance of our method with respect to classical alternatives.

### LAPLACIAN TRANSFORM BASED SPARSITY REGULARIZATION

"... The SENSE model with sparsity regularization acts as an unconstrained minimization problem to reconstruct the MRI, which obtain better reconstruction results than the traditional SENSE. To implement the sparsity constraints, discrete wavelet transform (DWT) and total variation (TV) are common exploi ..."

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The SENSE model with sparsity regularization acts as an unconstrained minimization problem to reconstruct the MRI, which obtain better reconstruction results than the traditional SENSE. To implement the sparsity constraints, discrete wavelet transform (DWT) and total variation (TV) are common exploited together to sparsify the MR image. In this paper, a novel sparsifying transform based on the combination of singular value decomposition (SVD) and Laplacian (LP) transform is proposed for parallel MR image reconstruction. The proposed algorithm adopts the SVD of the MR image as sparsifying transform instead of exploiting the wavelet domain sparsity of the image, and uses the LP-norm as an alternative to TV-norm in the sparsity regularization term. The performances of the proposed method are evaluated on two typical types of MR image (complex brain MR image and sparse angiogram MR image). Compared with the DWT-TV sparsifying transform, the proposed SVD-LP method can significantly achieve better reconstruction quality and considerably improve the computation efficiency.

### More IMPATIENT: A gridding-accelerated Toeplitz-based strategy for

"... journal homepage: www.elsevier.com/locate/jpdc ..."

### Magnetic Resonance Imaging: From Spin Physics to Medical Diagnosis

"... Abstract. Two rather similar historical evolutions are evoked, each one originating in fundamental spin studies by physicists, and ending as magnetic resonance imaging (MRI), a set of invaluable tools for clinical diagnosis in the hands of medical doctors. The first one starts with the early work on ..."

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Abstract. Two rather similar historical evolutions are evoked, each one originating in fundamental spin studies by physicists, and ending as magnetic resonance imaging (MRI), a set of invaluable tools for clinical diagnosis in the hands of medical doctors. The first one starts with the early work on nuclear magnetic resonance, the founding stone of the usual proton-based MRI, of which the basic principles are described. The second one starts with the optical pumping developments made to study the effects of spin polarization in various fundamental problems. Its unexpected outcome is a unique imaging modality, also based on MRI, for the study of lung physiology and pathologies. 1. Historical introduction Magnetic Resonance Imaging (MRI), now widely known for its usefulness as a medical diagnosis tool and for the variety of clear pictures of the body’s interior obtained in a harmless and non-invasive manner, had its foundations laid more than 60 years ago in physics experiments designed to measure properties of the nuclear spins of hydrogen atoms. In even earlier experiments, Rabi had shown that

### A Maximum Likelihood Approach to Parallel Imaging With Coil Sensitivity Noise

- IEEE TRANSACTIONS ON MEDICAL IMAGING

"... Parallel imaging is a powerful technique to speed up Magnetic Resonance (MR) image acquisition via multiple coils. Both the received signal of each coil and its sensitivity map, which describes its spatial response, are needed during reconstruction. Widely used schemes such as SENSE assume that sens ..."

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Parallel imaging is a powerful technique to speed up Magnetic Resonance (MR) image acquisition via multiple coils. Both the received signal of each coil and its sensitivity map, which describes its spatial response, are needed during reconstruction. Widely used schemes such as SENSE assume that sensitivity maps of the coils are noiseless while the only errors are due to a noisy signal. In practice, however sensitivity maps are subject to a wide variety of errors. At first glance, sensitivity noise appears to result in an errors-in-variables problem of the kind that is typically solved using Total Least Squares (TLS). However, existing TLS algorithms are inappropriate for the specific type of block structure that arises in parallel imaging. In this paper we take a maximum likelihood approach to the problem of parallel imaging in the presence of independent Gaussian sensitivity noise. This results in a quasi-quadratic objective function, which can be efficiently minimized. Experimental evidence suggests substantial gains over conventional SENSE, especially in non-ideal imaging conditions like low SNR, high g-factors, large acceleration and misaligned sensitivity maps.

### OPTIMIZATION OF A HIGH SENSITIVITY MRI RECEIVE COIL FOR PARALLEL HUMAN BRAIN IMAGING

"... Two eight-channel MRI receive-only coils were developed to provide whole-brain coverage at 1.5 T and 3.0 T field strength, respectively. Objectives were an image signal-to-noise ratio superior to standard designs throughout the human brain, as well as high parallel imaging performance. Electro-magne ..."

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Two eight-channel MRI receive-only coils were developed to provide whole-brain coverage at 1.5 T and 3.0 T field strength, respectively. Objectives were an image signal-to-noise ratio superior to standard designs throughout the human brain, as well as high parallel imaging performance. Electro-magnetic field simulations were used to determine array diameter and inter-element coil gap. Low mutual inductive coupling was achieved at 1.5 and 3.0 T using high-impedance pre-amplifiers. Coils show an average SNR improvement over commercial birdcage coils of 2.4 and 2.3 for the 1.5 T and 3.0 T design, respectively. The mean of the noise-amplification factor related to reconstruction of under-sampled data (gfactor) was 1.03 for 2-fold under-sampled data (rate-2) and 1.22 for rate-3 at 1.5 T. For data acquired with the 3.0 T coil array, these values were respectively 1.06 for rate-2 and 1.37 for rate-3. 1.

### unknown title

, 2005

"... Non-quadratic convex regularized reconstruction of MR images from spiral acquisitions ..."

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Non-quadratic convex regularized reconstruction of MR images from spiral acquisitions

### Fast Magnetic Resonance Imaging via Adaptive Broadband Encoding of the MR Signal Content

"... Abstract — Our goal is to increase the time-efficiency of continuous ..."