Approximate Message Passing with a Colored Aliasing Model for Variable Density Fourier Sampled Images

The Approximate Message Passing (AMP) algorithm efficiently reconstructs signals which have been sampled with large i.i.d. sub-Gaussian sensing matrices. Central to AMP is its "state evolution", which guarantees that the difference between the current estimate and ground truth (the "aliasing") at every iteration obeys a Gaussian distribution that can be fully characterized by a scalar. However, when Fourier coefficients of a signal with non-uniform spectral density are sampled, such as in Magnetic Resonance Imaging (MRI), the aliasing is intrinsically colored, AMP's scalar state evolution is no longer accurate and the algorithm encounters convergence problems. In response, we propose the Variable Density Approximate Message Passing (VDAMP) algorithm, which uses the wavelet domain to model the colored aliasing. We present empirical evidence that VDAMP obeys a "colored state evolution", where the aliasing obeys a Gaussian distribution that can be fully characterized with one scalar per wavelet subband. A benefit of state evolution is that Stein's Unbiased Risk Estimate (SURE) can be effectively implemented, yielding an algorithm with subband-dependent thresholding that has no free parameters. We empirically evaluate the effectiveness of VDAMP on three variations of Fast Iterative Shrinkage-Thresholding (FISTA) and find that it converges in around 10 times fewer iterations on average than the next-fastest method, and to a comparable mean-squared-error.Comment: 13 pages, 7 figures, 3 tables. arXiv admin note: text overlap with arXiv:1911.0123

An Approximate Message Passing Algorithm for Rapid Parameter-Free Compressed Sensing MRI

For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with variable density, AMP encounters convergence problems. In response we present an algorithm based on Orthogonal AMP constructed specifically for variable density partial Fourier sensing matrices. For the first time in this setting a state evolution has been observed. A practical advantage of state evolution is that Stein's Unbiased Risk Estimate (SURE) can be effectively implemented, yielding an algorithm with no free parameters. We empirically evaluate the effectiveness of the parameter-free algorithm on simulated data and find that it converges over 5x faster and to a lower mean-squared error solution than Fast Iterative Shrinkage-Thresholding (FISTA).Comment: 5 pages, 5 figures, IEEE International Conference on Image Processing (ICIP) 202

INK-SVD: Learning incoherent dictionaries for sparse representations

This work considers the problem of learning an incoherent dictionary that is both adapted to a set of training data and incoherent so that existing sparse approximation algorithms can recover the sparsest representation. A new decorrelation method is presented that computes a fixed coherence dictionary close to a given dictionary. That step iterates pairwise decorrelations of atoms in the dictionary. Dictionary learning is then performed by adding this decorrelation method as an intermediate step in the K-SVD learning algorithm. The proposed algorithm INK-SVD is tested on musical data and compared to another existing decorrelation method. INK-SVD can compute a dictionary that approximates the training data as well as K-SVD while decreasing the coherence from 0.6 to 0.2. © 2012 IEEE

On the Use of Infrared Thermography for the Estimation of Melting Enthalpy

A calorimetry method based on infrared thermography is showing promise for material screening, allowing the simultaneous detection of phase transitions of multiple samples at a time, hence enabling the establishment of phase diagrams in a record time. The working principle of this method is similar to the one of Differential Thermal Analysis. Therefore, this work aims at identifying if the melting enthalpy of materials could be estimated on the same basis using infrared thermography. In this work, the melting of six eutectic mixtures of fatty acids is estimated under three considerations. The results are compared to Differential Scanning Calorimetry measurements and literature data. The accuracy of the method is discussed and improvements are proposed

Applicability of Infrared Thermography for the Detection of Phase Transitions in Metal Alloys

This work aims at assessing the applicability of a screening-oriented device dedicated to the establishment of increasingly complex phase diagrams of phase change materials. A thermography-based method has recently been proven to allow the detection of phase transitions of organic materials for multiple samples at a time. The phase transition detection capability of the infrared thermography method is here evaluated for metal systems based on well-referenced materials commonly employed in DSC calibration (pure sample of Gallium and a mixture of Gallium and Indium). The detected transitions are compared to literature data and DSC measurements. All transitions documented in the literature could be retrieved by thermography, and liquidus transitions are validated with DSC measurements. The encouraging nature of the results is discussed, and avenues for improving the method are considered

LocOMP: algorithme localement orthogonal pour l'approximation parcimonieuse rapide de signaux longs sur des dictionnaires locaux

National audienceCet article présente LocOMP, un algorithme d'approximation parcimonieuse rapide pour les dictionnaires locaux (en particulier, les dictionnaires invariants par translation comme les dictionnaires temps-fréquence). Expérimentalement, LocOMP fournit des approximations aussi bonnes qu'OMP tout en restant dans la même classe de complexité que MP. C'est à notre connaissance le premier algorithme plus évolué que MP utilisable sur des signaux longs. LocOMP s'est montré expérimentalement 500 fois plus rapide qu'OMP

Learning a Probabilistic Model for Diffeomorphic Registration

International audienceWe propose to learn a low-dimensional probabilistic deformation model from data which can be used for registration and the analysis of deformations. The latent variable model maps similar deformations close to each other in an encoding space. It enables to compare deformations, generate normal or pathological deformations for any new image or to transport deformations from one image pair to any other image. Our unsupervised method is based on variational inference. In particular, we use a conditional variational autoencoder (CVAE) network and constrain transformations to be symmetric and diffeomorphic by applying a differentiable exponentiation layer with a symmetric loss function. We also present a formulation that includes spatial regularization such as diffusion-based filters. Additionally, our framework provides multi-scale velocity field estimations. We evaluated our method on 3-D intra-subject registration using 334 cardiac cine-MRIs. On this dataset, our method showed state-of-the-art performance with a mean DICE score of 81.2% and a mean Hausdorff distance of 7.3mm using 32 latent dimensions compared to three state-of-the-art methods while also demonstrating more regular deformation fields. The average time per registration was 0.32s. Besides, we visualized the learned latent space and show that the encoded deformations can be used to transport deformations and to cluster diseases with a classification accuracy of 83% after applying a linear projection

Learning a Probabilistic Model for Diffeomorphic Registration

International audienceWe propose to learn a low-dimensional probabilistic deformation model from data which can be used for registration and the analysis of deformations. The latent variable model maps similar deformations close to each other in an encoding space. It enables to compare deformations, generate normal or pathological deformations for any new image or to transport deformations from one image pair to any other image. Our unsupervised method is based on variational inference. In particular, we use a conditional variational autoencoder (CVAE) network and constrain transformations to be symmetric and diffeomorphic by applying a differentiable exponentiation layer with a symmetric loss function. We also present a formulation that includes spatial regularization such as diffusion-based filters. Additionally, our framework provides multi-scale velocity field estimations. We evaluated our method on 3-D intra-subject registration using 334 cardiac cine-MRIs. On this dataset, our method showed state-of-the-art performance with a mean DICE score of 81.2% and a mean Hausdorff distance of 7.3mm using 32 latent dimensions compared to three state-of-the-art methods while also demonstrating more regular deformation fields. The average time per registration was 0.32s. Besides, we visualized the learned latent space and show that the encoded deformations can be used to transport deformations and to cluster diseases with a classification accuracy of 83% after applying a linear projection

Characterization of Fatty Acids as Biobased Organic Materials for Latent Heat Storage

This work aims to characterize phase change materials (PCM) for thermal energy storage in buildings (thermal comfort). Fatty acids, biobased organic PCM, are attractive candidates for integration into active or passive storage systems for targeted application. Three pure fatty acids (capric, myristic and palmitic acids) and two eutectic mixtures (capric-myristic and capric-palmitic acids) are studied in this paper. Although the main storage properties of pure fatty acids have already been investigated and reported in the literature, the information available on the eutectic mixtures is very limited (only melting temperature and enthalpy). This paper presents a complete experimental characterization of these pure and mixed fatty acids, including measurements of their main thermophysical properties (melting temperature and enthalpy, specific heats and densities in solid and liquid states, thermal conductivity, thermal diffusivity as well as viscosity) and the properties of interest regarding the system integrating the PCM (energy density, volume expansion). The storage performances of the studied mixtures are also compared to those of most commonly used PCM (salt hydrates and paraffins).This research work was developed in the framework of SUDOKET project (Interreg Sudoe SOE2/P1/E0677). The authors are grateful to the European Regional Development Fund (ERDF) to co-fund the project through the Interreg Sudoe Programme and the Region Nouvelle Aquitaine for subsidizing BioMCP project (Project-2017-1R10209-13023). The authors would also like to extend their thanks to CNRS for promoting the I2M Bordeaux-CICenergiGUNE exchanges in the framework of the IEA PHASE-IR project