scholarly journals Binary Sparse Phase Retrieval via Simulated Annealing

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Wei Peng ◽  
Hongxia Wang
Keyword(s):  
Fourier Transform ◽  
Simulated Annealing ◽  
Recovery Rate ◽  
Phase Retrieval ◽  
High Recovery ◽  
Phase Recovery ◽  
Greedy Strategy ◽  
High Recovery Rate ◽  
Binary Model ◽  
The Fourier Transform

This paper presents the Simulated Annealing Sparse PhAse Recovery (SASPAR) algorithm for reconstructing sparse binary signals from their phaseless magnitudes of the Fourier transform. The greedy strategy version is also proposed for a comparison, which is a parameter-free algorithm. Sufficient numeric simulations indicate that our method is quite effective and suggest the binary model is robust. The SASPAR algorithm seems competitive to the existing methods for its efficiency and high recovery rate even with fewer Fourier measurements.

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

FACIAL PARALYSIS IN CHILDREN

PEDIATRICS ◽  
1957 ◽  
Vol 19 (2) ◽  
pp. 303-316
Author(s):  
Richmond S. Paine
Keyword(s):  
Facial Paralysis ◽  
Recovery Rate ◽  
Recovery Time ◽  
Surgical Decompression ◽  
Careful Study ◽  
High Recovery ◽  
Prompt Treatment ◽  
The Past ◽  
High Recovery Rate ◽  
Methods Of Treatment

The anatomy of the facial nerve and the various etiologic factors in both congenital and acquired facial paralysis in children have been reviewed. Differential diagnosis among the more important of these has been discussed and an evaluation of the possible methods of treatment attempted. This evaluation is difficult because of the high recovery rate without treatment, which may approach 90% in children. If careful study of a case of facial paralysis indicates its idiopathic nature, prompt treatment with oral cortisone is considered indicated. While it is difficult to establish that cortisone greatly improved an already high recovery rate, it seems more clear that the average recovery time is favorably influenced, at least in adults and probably also in children. Cortisone seems the treatment of choice at the present time and during the past 2 years at one hospital, all of 10 patients so treated recovered. This has eliminated the need for consideration of surgical decompression of the facial canal. Whether this will remain true with larger numbers of cases remains to be seen.

Research of Purifying Alkali Weight-Reduction Wastewater to Recovery of Terephthalic Acid

2011 ◽  
Vol 183-185 ◽  
pp. 110-114
Author(s):  
Chao Nan Liu ◽  
Wei Hong Xia
Keyword(s):  
Sustainable Development ◽  
Weight Reduction ◽  
Recovery Rate ◽  
Terephthalic Acid ◽  
Industrial Wastewater ◽  
Cod Removal ◽  
Valuable Resource ◽  
High Recovery ◽  
High Recovery Rate

In those traditional ways of treating alkali weight-reduction wastewater, the COD removal is greatly considered, while recovering terephthalic acid (TA) by valuable resource according to the principles of sustainable development is less involved. In this research, recovery of high pure TA from alkali weight-reduction has been researched by purified mother liquid with coagulation-sedimentation. The purity of TA obtained was investigated by various methods, results has shown that the characters of TA was great improved in view of high recovery rate by coagulation-sedimentation on conditions of pH 7.0-8.0 of wastewater and 200-250mg/l in quantity of PAC, so coagulation-sedimentation by pretreatment is an effective method. The study is also very useful in recycling of PET or treating TA industrial wastewater.

scholarly journals Significant Waning of Active Cases of Covid-19 With High Recovery After Three Months of Complete Lockdown: Plausible Implication On Emergence of Herd Immunity in The Population

2020 ◽  
Vol 3 (3) ◽  
Keyword(s):  
Recovery Rate ◽  
Protective Immunity ◽  
Infectious Virus ◽  
Herd Immunity ◽  
Therapeutic Agents ◽  
High Recovery ◽  
Rate Of Spread ◽  
High Recovery Rate ◽  
Rapid Fall ◽  
Fast Spreading

COVID-19 is fast spreading around the globe in a highly contagious manner. Until date there are no therapeutic agents/vaccines developed which could control this highly infectious virus from spreading among human population. Our earlier studies showed that implementation of prolonged lockdown had a profound effect on the rate of spread of COVID-19 in the population. The observed increase in doubling time of COVID-19 with a high recovery rate following complete Lockdown reflected that protective immunity may be present in the population. In this article, the data from three months following completion of Lockdown was considered. The results reflected that there was a significant down trend in the rate of COVID-19 with high recovery rate reaching up to 83% of the affected cases of COVID-19 by September 30, 2020. The projection made from the data up to 30 November, 2020, pointed towards continued decrease in active cases of COVID-19. Concomitant with this result, the recovery from COVID-19 reached to ~90% by end of October, 2020. The significance of the above mentioned results with rapid fall in active cases from end of September 30, 2020, in spite of increased testing for COVID-19 in generating immunity against COVID-19 is discussed.

scholarly journals A Sharp Rearrangement Principle in Fourier Space and Symmetry Results for PDEs with Arbitrary Order

2020 ◽  
Author(s):  
Enno Lenzmann ◽  
Jérémy Sok
Keyword(s):  
Fourier Transform ◽  
Phase Retrieval ◽  
Differential Operators ◽  
Arbitrary Order ◽  
Radial Symmetry ◽  
Fourier Space ◽  
Polyharmonic Operator ◽  
Pseudo Differential Operators ◽  
Retrieval Problem ◽  
The Fourier Transform

Abstract We prove sharp inequalities for the symmetric-decreasing rearrangement in Fourier space of functions in $\mathbb{R}^d$. Our main result can be applied to a general class of (pseudo-)differential operators in $\mathbb{R}^d$ of arbitrary order with radial Fourier multipliers. For example, we can take any positive power of the Laplacian $(-\Delta )^s$ with $s> 0$ and, in particular, any polyharmonic operator $(-\Delta )^m$ with integer $m \geqslant 1$. As applications, we prove radial symmetry and real-valuedness (up to trivial symmetries) of optimizers for (1) Gagliardo–Nirenberg inequalities with derivatives of arbitrary order, (2) ground states for bi- and polyharmonic nonlinear Schrödinger equations (NLS), and (3) Adams–Moser–Trudinger type inequalities for $H^{d/2}(\mathbb{R}^d)$ in any dimension $d \geqslant 1$. As a technical key result, we solve a phase retrieval problem for the Fourier transform in $\mathbb{R}^d$. To achieve this, we classify the case of equality in the corresponding Hardy–Littlewood majorant problem for the Fourier transform in $\mathbb{R}^d$.

scholarly journals Simultaneously Recovering High-Purity Chromium and Removing Organic Pollutants from Tannery Effluent

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Jie Zong ◽  
Yan-Chun Li ◽  
Kang Hu
Keyword(s):  
High Purity ◽  
Recovery Rate ◽  
Fenton Oxidation ◽  
Tannery Effluent ◽  
High Recovery ◽  
Chromium Powder ◽  
Tannery Waste ◽  
High Recovery Rate ◽  
Chrome Tanning ◽  
Grain Surface

Chromium pollution is a serious issue because of carcinogenic toxicities of the pollutants and low recovery rate of chromium because of the presence of organic, such as protein and fat. In this work, high recovery rate and high purity of the chromium ion were successfully prepared by the way of acid enzyme, flocculant, and Fenton oxidation. The experiments were characterized by TG, TOC, UV-VIS, and SEM. In the work, the tannery waste chrome liquor was used as experimental material. The results showed that the percentage of reduction of TOC in the tannery waste chrome liquor by method of Fenton oxidation, acid enzyme, and the flocculant was 71.15%, 65.26%, and 22.05%, respectively. Therefore, the organism content of chrome tanning waste liquid was greatly reduced through the pretreatment. And the application experiment showed that the properties and grain surface and fibers of the tanned leather with commercial chromium powder and chrome tanning agent prepared from the chromium waste liquid treated with Fenton are nearly the same.

scholarly journals FISHING ACTIVITY, SIZE DISTRIBUTION, TAG RELEASED AND RECAPTURE OF TUNA TAGGING IN EASTERN INDONESIAN WATERS

2012 ◽  
Vol 18 (1) ◽  
pp. 47 ◽  
Author(s):  
Moh. Natsir ◽  
Anung Widodo ◽  
Budi Iskandar Prisantoso
Keyword(s):  
Recovery Rate ◽  
Size Range ◽  
Stock Assessment ◽  
Survey Area ◽  
Length Frequency ◽  
Biological Aspect ◽  
High Recovery ◽  
Fishing Activity ◽  
High Recovery Rate ◽  
Collaborative Program

Tagging of tropical tunas has a long history in Indonesian waters. Since 1987 tuna tagging has been conducted in Indonesian Waters. Tuna tagging in 2008 in eastern Indonesian waters was conducted in collaborative program with SPC to obtain new data about biological aspect and stock assessment of tuna. This tuna tagging was successfully conducted at 86 locations, with a total of 25,197 tuna tagged with conventional tags, at an average of around 900 fish per fishing day. The releases of conventional tags comprised of 19,576 skipjack (77.7%), 5,267 yellowfin (20.9%) and 354 bigeye (1.4%). From the length frequency composition, the skipjack size range was wide, between 29 – 83 cm, but mostly between 35 and 40 cm with 38.9 cm average. The yellowfin size range of 28 – 65 cm, with most fish between 37 and 41 cm of 40.1 cm average. The small numbers of bigeye tagged were mostly larger than 38 cm, ranging from 29 to 58 cm with 41.3 cm average. During the tagging<br />cruise, bait fish to support the fishing activity was relatively easily found in and around the survey area, either with direct catching using bouke ami net or purchasing from the lift net fisherman. By the end of 2010, 4,594 tags was recovered representing a relatively high recovery rate of 18.2% overall.

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