Imaging with highly incomplete and corrupted data

We consider the problem of imaging sparse scenes from a few noisy data using an L1-minimization approach. This problem can be cast as a linear system of the form Ap = b, where A is an N x K measurement matrix. We assume that the dimension of the unknown sparse vector p E Ck is much larger than the dimension of the data vector b E Cn, i.e. K >>N. We provide a theoretical framework that allows us to examine under what conditions the L1-minimization problem admits a solution that is close to the exact one in the presence of noise. Our analysis shows that L1-minimization is not robust for imaging with noisy data when high resolution is required. To improve the performance of L1-minimization we propose to solve instead the augmented linear system [A|C]p = b, where the N = Σ matrix C is a noise collector. It is constructed so as its column vectors provide a frame on which the noise of the data, a vector of dimension N, can be well approximated. Theoretically, the dimension Σ of the noise collector should be eN which would make its use not practical. However, our numerical results illustrate that robust results in the presence of noise can be obtained with a large enough number of columns Σ~10K.Part of this material is based upon work supported by the National Science Foundation under Grant No. DMS-1439786 while the authors were in residence at the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, RI, during the Fall 2017 semester. The work of M Moscoso was partially supported by Spanish MICINN grant FIS2016-77892-R. The work of A Novikov was partially supported by NSF grants DMS-1515187, DMS-1813943. The work of C Tsogka was partially supported by AFOSR FA9550-17-1-0238

Multi-ancestry study of blood lipid levels identifies four loci interacting with physical activity.

Many genetic loci affect circulating lipid levels, but it remains unknown whether lifestyle factors, such as physical activity, modify these genetic effects. To identify lipid loci interacting with physical activity, we performed genome-wide analyses of circulating HDL cholesterol, LDL cholesterol, and triglyceride levels in up to 120,979 individuals of European, African, Asian, Hispanic, and Brazilian ancestry, with follow-up of suggestive associations in an additional 131,012 individuals. We find four loci, in/near CLASP1, LHX1, SNTA1, and CNTNAP2, that are associated with circulating lipid levels through interaction with physical activity; higher levels of physical activity enhance the HDL cholesterol-increasing effects of the CLASP1, LHX1, and SNTA1 loci and attenuate the LDL cholesterol-increasing effect of the CNTNAP2 locus. The CLASP1, LHX1, and SNTA1 regions harbor genes linked to muscle function and lipid metabolism. Our results elucidate the role of physical activity interactions in the genetic contribution to blood lipid levels

Multi-ancestry study of blood lipid levels identifies four loci interacting with physical activity

The present work was largely supported by a grant from the US National Heart, Lung, and Blood Institute (NHLBI) of the National Institutes of Health (R01HL118305). The full list of acknowledgments appears in the Supplementary Notes 3 and 4.Peer reviewedPublisher PD

Quantitative phase and absorption contrast imaging

We present an algorithm for coherent diffractive imaging with phaseless measurements. It treats the forward model as a combination of coherent and incoherent waves. The algorithm reconstructs absorption and phase contrast that quantifies the attenuation and the refraction of the waves propagating through an object. It requires coherent or partially coherent illuminations, and several detectors to record the intensity of the distorted wave that passes through the object under inspection. The diversity of illuminations, obtained by putting masks between the source and the object, provides enough information for imaging. The computational cost of our algorithm is linear in the number of pixels of the image. Therefore, it is efficient for high-resolution imaging. Our algorithm guarantees exact recovery if the image is sparse for a given basis. Numerical experiments in the setting of phaseless diffraction imaging of sparse objects validate the efficiency and the precision of the suggested algorithm.The work of Miguel Moscoso was supported by the Grant PID2020-115088RB-I00. The work of Alexei Novikov was supported in part by NSF under Grant DMS-1813943 and in part by AFOSR under Grant FA9550-20-1-0026. The work of Chrysoula Tsogka was supported by AFOSR under Grant FA9550-21-1-0196

Fast signal recovery from quadratic measurements

We present a novel approach for recovering a sparse signal from quadratic measurements corresponding to a rank-one tensorization of the data vector. Such quadratic measurements, referred to as interferometric or cross-correlated data, naturally arise in many fields such as remote sensing, spectroscopy, holography and seismology. Compared to the sparse signal recovery problem that uses linear measurements, the unknown in this case is a matrix formed by the cross correlations of the sought signal. This creates a bottleneck for the inversion since the number of unknowns grows quadratically with the dimension of the signal. The main idea of the proposed approach is to reduce the dimensionality of the problem by recovering only the diagonal of the unknown matrix, whose dimension grows linearly with the size of the signal, and use an efficient Noise Collector to absorb the cross-correlated data that come from the off-diagonal elements of this matrix. These elements do not carry extra information about the support of the signal, but significantly contribute to these data. With this strategy, we recover the unknown matrix by solving a convex linear problem whose cost is similar to the one that uses linear measurements. Our theory shows that the proposed approach provides exact support recovery when the data is not too noisy, and that there are no false positives for any level of noise. It also demonstrates that the level of sparsity that can be recovered scales almost linearly with the number of data. The numerical experiments presented in the paper corroborate these findings.The work of Miguel Moscoso was supported by Spanish MICINN under Grant FIS2016-77892-R. The work of Alexei Novikov was supported by NSF DMS under Grant 1813943 and AFOSR under Grant FA9550-20-1-0026. The work of George Papanicolaou was supported by AFOSR under Grant FA9550-18-1-0519. The work of Chrysoula Tsogka was supported by AFOSR under Grants FA9550-17-1-0238 and FA9550-18-1-0519

Multiset correlation and factor analysis enables exploration of multi-omics data.

Multi-omics datasets are becoming more common, necessitating better integration methods to realize their revolutionary potential. Here, we introduce multi-set correlation and factor analysis (MCFA), an unsupervised integration method tailored to the unique challenges of high-dimensional genomics data that enables fast inference of shared and private factors. We used MCFA to integrate methylation markers, protein expression, RNA expression, and metabolite levels in 614 diverse samples from the Trans-Omics for Precision Medicine/Multi-Ethnic Study of Atherosclerosis multi-omics pilot. Samples cluster strongly by ancestry in the shared space, even in the absence of genetic information, while private spaces frequently capture dataset-specific technical variation. Finally, we integrated genetic data by conducting a genome-wide association study (GWAS) of our inferred factors, observing that several factors are enriched for GWAS hits and trans-expression quantitative trait loci. Two of these factors appear to be related to metabolic disease. Our study provides a foundation and framework for further integrative analysis of ever larger multi-modal genomic datasets

Proliferative potential and response to nivolumab in clear cell renal cell carcinoma patients.

BackgroundBiomarkers predicting immunotherapy response in metastatic renal cell cancer (mRCC) are lacking. PD-L1 immunohistochemistry is a complementary diagnostic for immune checkpoint inhibitors (ICIs) in mRCC, but has shown minimal clinical utility and is not used in routine clinical practice.MethodsTumor specimens from 56 patients with mRCC who received nivolumab were evaluated for PD-L1, cell proliferation (targeted RNA-seq), and outcome.ResultsFor 56 patients treated with nivolumab as a standard of care, there were 2 complete responses and 8 partial responses for a response rate of 17.9%. Dividing cell proliferation into tertiles, derived from the mean expression of 10 proliferation-associated genes in a reference set of tumors, poorly proliferative tumors (62.5%) were more common than moderately (30.4%) or highly proliferative (8.9%) counterparts. Moderately proliferative tumors were enriched for PD-L1 positive (41.2%), compared to poorly proliferative counterparts (11.4%). Objective response for moderately proliferative (29.4%) tumors was higher than that of poorly (11.4%) proliferative counterparts, but not statistically significant (p = .11). When cell proliferation and negative PD-L1 tumor proportion scores were combined statistically significant results were achieved (p = .048), showing that patients with poorly proliferative and PD-L1 negative tumors have a very low response rate (6.5%) compared to moderately proliferative PD-L1 negative tumors (30%).ConclusionsCell proliferation has value in predicting response to nivolumab in clear cell mRCC patients, especially when combined with PD-L1 expression. Further studies which include the addition of progression-free survival (PFS) along with sufficiently powered subgroups are required to further support these findings