Unrolled primal-dual networks for lensless cameras

Conventional models for lensless imaging assume that each measurement results from convolving a given scene with a single experimentally measured point-spread function. These models fail to simulate lensless cameras truthfully, as these models do not account for optical aberrations or scenes with depth variations. Our work shows that learning a supervised primal-dual reconstruction method results in image quality matching state of the art in the literature without demanding a large network capacity. We show that embedding learnable forward and adjoint models improves the reconstruction quality of lensless images (+5dB PSNR) compared to works that assume a fixed point-spread function

Effects of activated lactoperoxidase system on microbiological quality of raw milk

The poor microbiological quality of raw cow milk in Turkey is a major concern. It has been speculated that less activation of naturally present lactoperoxidase system in the milk is the reason for its poor microbiological quality. Hence, the objective of this study was to investigate the effects of activation of the lactoperoxidase (LP) system on microbiological quality of the raw milk. The milk samples collected from a dairy farm were analyzed in the laboratory by dividing into two equal parts as activated (experimental) and control group. The experimental group was activated by treatment with equal concentration of sodium thiocyanate and hydrogen peroxide (20:20 mg/kg) whereas the control sample remained unactivated. All samples were stored at 4°C during 12 h. The microbial load in all the samples was quantitatively determined at 0, 3, 6, 9 and 12 h. The quantitative changes in each microbial species in both growth were recorded and statistically analyzed. The initial count of total mesophilic aerobic bacteria, psychrotroph bacteria, Pseudomonas spp., Enterobacteriaceae and yeast number were 7.10, 5.14, 6.42, 5.93 and 4.31 log cfu/mL, respectively, and at the end of 3 h the counts were 0.43, 2.23, 1.09, 0.93 and 0.37 log cfu/mL, respectively, were lower than controls. Significant (P<0.05) differences were observed for microbial count of activated and control samples except in case of lactic acid bacteria. The results of this study indicate that the addition of thiocyanate and hydrogen peroxidase to the milk activated lactoperoxidase enzyme already present in the milk and slowed down the microbiological growth, especially of the reducing proteolytic Pseudomonas spp. On comparison, the results for total mesophilic aerobic bacteria, psychrotroph bacteria, Pseudomonas spp., Enterobacteriaceae and yeast were statistically significant (P<0.05) and no significant change was observed in case of lactic acid bacteria

Difference system for Selberg correlation integrals

The Selberg correlation integrals are averages of the products $\prod_{s=1}^m\prod_{l=1}^n (x_s - z_l)^{\mu_s}$ with respect to the Selberg density. Our interest is in the case $m=1$, $\mu_1 = \mu$, when this corresponds to the $\mu$-th moment of the corresponding characteristic polynomial. We give the explicit form of a $(n+1) \times (n+1)$ matrix linear difference system in the variable $\mu$ which determines the average, and we give the Gauss decomposition of the corresponding $(n+1) \times (n+1)$ matrix. For $\mu$ a positive integer the difference system can be used to efficiently compute the power series defined by this average.Comment: 21 page

On the functions counting walks with small steps in the quarter plane

Models of spatially homogeneous walks in the quarter plane ${\bf Z}_+^{2}$ with steps taken from a subset $\mathcal{S}$ of the set of jumps to the eight nearest neighbors are considered. The generating function $(x,y,z)\mapsto Q(x,y;z)$ of the numbers $q(i,j;n)$ of such walks starting at the origin and ending at $(i,j) \in {\bf Z}_+^{2}$ after $n$ steps is studied. For all non-singular models of walks, the functions $x \mapsto Q(x,0;z)$ and $y\mapsto Q(0,y;z)$ are continued as multi-valued functions on ${\bf C}$ having infinitely many meromorphic branches, of which the set of poles is identified. The nature of these functions is derived from this result: namely, for all the 51 walks which admit a certain infinite group of birational transformations of ${\bf C}^2$, the interval $]0,1/|\mathcal{S}|[$ of variation of $z$ splits into two dense subsets such that the functions $x \mapsto Q(x,0;z)$ and $y\mapsto Q(0,y;z)$ are shown to be holonomic for any $z$ from the one of them and non-holonomic for any $z$ from the other. This entails the non-holonomy of $(x,y,z)\mapsto Q(x,y;z)$, and therefore proves a conjecture of Bousquet-M\'elou and Mishna.Comment: 40 pages, 17 figure

Solving Phase Retrieval with a Learned Reference

Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by leveraging some prior knowledge about the structure of the unknown image. The inherent ambiguities about shift and flip in the Fourier measurements make this problem especially difficult; and most of the existing methods use several random restarts with different permutations. In this paper, we assume that a known (learned) reference is added to the signal before capturing the Fourier amplitude measurements. Our method is inspired by the principle of adding a reference signal in holography. To recover the signal, we implement an iterative phase retrieval method as an unrolled network. Then we use back propagation to learn the reference that provides us the best reconstruction for a fixed number of phase retrieval iterations. We performed a number of simulations on a variety of datasets under different conditions and found that our proposed method for phase retrieval via unrolled network and learned reference provides near-perfect recovery at fixed (small) computational cost. We compared our method with standard Fourier phase retrieval methods and observed significant performance enhancement using the learned reference.Comment: Accepted to ECCV 2020. Code is available at https://github.com/CSIPlab/learnPR_referenc

Symphytum Species: A Comprehensive Review on Chemical Composition, Food Applications and Phytopharmacology

Symphytum species belongs to the Boraginaceae family and have been used for centuries for bone breakages, sprains and rheumatism, liver problems, gastritis, ulcers, skin problems, joint pain and contusions, wounds, gout, hematomas and thrombophlebitis. Considering the innumerable potentialities of the Symphytum species and their widespread use in the world, it is extremely important to provide data compiling the available literature to identify the areas of intense research and the main gaps in order to design future studies. The present review aims at summarizing the main data on the therapeutic indications of the Symphytum species based on the current evidence, also emphasizing data on both the e cacy and adverse e ects. The present review was carried out by consulting PubMed (Medline), Web of Science, Embase, Scopus, Cochrane Database, Science Direct and Google Scholar (as a search engine) databases to retrieve the most updated articles on this topic. All articles were carefully analyzed by the authors to assess their strengths and weaknesses, and to select the most useful ones for the purpose of review, prioritizing articles published from 1956 to 2018. The pharmacological e ects of the Symphytum species are attributed to several chemical compounds, among them allantoin, phenolic compounds, glycopeptides, polysaccharides and some toxic pyrrolizidine alkaloids. Not less important to highlight are the risks associated with its use. In fact, there is increasing consumption of over-the-counter drugs, which when associated with conventional drugs can cause serious and even fatal adverse events. Although clinical trials sustain the folk topical application of Symphytum species in musculoskeletal and blunt injuries, with minor adverse e ects, its antimicrobial potency was still poorly investigated. Further studies are needed to assess the antimicrobial spectrum of Symphytum species and to characterize the active molecules both in vitro and in vivo

Fast construction of irreducible polynomials over finite fields

International audienceWe present a randomized algorithm that on input a finite field $K$ with $q$ elements and a positive integer $d$ outputs a degree $d$ irreducible polynomial in $K[x]$. The running time is $d^{1+o(1)} \times (\log q)^{5+o(1)}$ elementary operations. The $o(1)$ in $d^{1+o(1)}$ is a function of $d$ that tends to zero when $d$ tends to infinity. And the $o(1)$ in $(\log q)^{5+o(1)}$ is a function of $q$ that tends to zero when $q$ tends to infinity. In particular, the complexity is quasi-linear in the degree $d$