Phase retrieval from power spectra of masked signals

In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein have found limited success. One alternative is to create redundancy in the measurement process by illuminating the signal multiple times, distorting the signal each time with a different mask. Despite several recent advances in phase retrieval, the community has yet to construct an ensemble of masks which uniquely determines all signals and admits an efficient reconstruction algorithm. In this paper, we leverage the recently proposed polarization method to construct such an ensemble. We also present numerical simulations to illustrate the stability of the polarization method in this setting. In comparison to a state-of-the-art phase retrieval algorithm known as PhaseLift, we find that polarization is much faster with comparable stability.Comment: 18 pages, 3 figure

Phase retrieval with polarization

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a novel measurement design which is inspired by interferometry and exploits certain properties of expander graphs. We also give an efficient phase retrieval procedure, and use recent results in spectral graph theory to produce a stable performance guarantee which rivals the guarantee for PhaseLift in [Candes et al. 2011]. We use numerical simulations to illustrate the performance of our phase retrieval procedure, and we compare reconstruction error and runtime with a common alternating-projections-type procedure

Saving phase: Injectivity and stability for phase retrieval

Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every signal up to a global phase factor, and how many are needed to do so? Furthermore, which measurement ensembles lend stability? This paper presents several results that address each of these questions. We begin by characterizing injectivity, and we identify that the complement property is indeed a necessary condition in the complex case. We then pose a conjecture that 4M-4 generic measurement vectors are both necessary and sufficient for injectivity in M dimensions, and we prove this conjecture in the special cases where M=2,3. Next, we shift our attention to stability, both in the worst and average cases. Here, we characterize worst-case stability in the real case by introducing a numerical version of the complement property. This new property bears some resemblance to the restricted isometry property of compressed sensing and can be used to derive a sharp lower Lipschitz bound on the intensity measurement mapping. Localized frames are shown to lack this property (suggesting instability), whereas Gaussian random measurements are shown to satisfy this property with high probability. We conclude by presenting results that use a stochastic noise model in both the real and complex cases, and we leverage Cramer-Rao lower bounds to identify stability with stronger versions of the injectivity characterizations.Comment: 22 page

Modified Social Benches: Exploring the Role of Aesthetic Interaction to Placemaking

This paper discusses some aesthetic and social aspects that involve interactions with urban art installations. The aim is to better understand how, and to what extent, aesthetic interactions with art installations can transform an urban space into a place. The discussion is based on a case study of the Modified Social Benches, a series of outdoor, interactive artworks that provide different types of bodily engagement, social encounters and aesthetic experiences. A detailed empirical analysis is carried out, emphasising the social roles around the installations as well as the most salient aspects regarding the bodily, the spatial and the experiential qualities of the interactions. The results suggest that urban installations affording playful, action-oriented and sensorimotor encounters are more effective to placemaking than installations that encourage static modalities of social activities

Certifying the restricted isometry property is hard

This paper is concerned with an important matrix condition in compressed sensing known as the restricted isometry property (RIP). We demonstrate that testing whether a matrix satisfies RIP is NP-hard. As a consequence of our result, it is impossible to efficiently test for RIP provided P \neq NP

The financial sustainability of Microcredit in Portugal

Microcredit and microfinance emerged in the 1970’s in Bangladesh and other developing countries and expanded rapidly worldwide as a business model financially sustainable and able to fight poverty and social exclusion. Empirical evidence confirms microcredit ability to mitigate poverty but its financial sustainability is controversial. Using 2006-2009 Portuguese micro-level data, we estimate the failure rate of Portuguese micro-credit projects as 20,6%/year that, to be financially sustainable, would require a real interest rate by 25%/year. Using a territorial variable on a discrete Cox proportional hazard model with censured data, we estimate that the failure rate of those micro-credit projects located in the worst-case NUTS II Portuguese regions (Alentejo and Centro) and promoted by lower schooling people is significantly higher than best-case.Microcredit, Firms failure rate, Poverty, Financial sustainability

Relação entre medidas de resultados centrados na pessoa e medidas clínicas convencionais em indivíduos com osteoartrose do joelho

OBJECTIVOS: Analisar a relação entre medidas clínicas convencionais da fisioterapia, testes funcionais e medidas genéricas e de condição específica do estado de saúde, bem como examinar o poder preditivo das medidas clínicas convencionais e dos testes funcionais nas medidas genéricas e de condição específica do estado de saúde, em indivíduos com osteoartrose (OA) do joelho. RELEVÂNCIA: Os resultados dos cuidados de fisioterapia prestados a indivíduos com OA do joelho são vulgarmente medidos através de medidas clínicas convencionais e testes funcionais, embora não se conheça claramente a adequação destas medidas para estimar a percepção global do indivíduo face ao seu estado de saúde. AMOSTRA: Participaram 37 pessoas (sexo: 25 mulheres, 12 homens; idade: 67,6±9,05 anos; estatura:161,3±6,8 cm; peso: 77,3±13.1 kg com OA do joelho. METODOLOGIA: as medidas clínicas avaliadas foram o teste muscular, a goniometria, a medição do ângulo Q. Foram administrados os testes funcionais de subir e descer escadas e o Timed Up & Go Test. O estado de saúde foi medido com os questionários MOS SF-36 e WOMAC. ANÁLISE ESTATÍSTICA: O coeficiente r de Pearson foi utilizado para analisar as relações entre as diferentes medidas de resultados. A análise de regressão (forward stepwise regression) foi utilizada para identificar as medidas clínicas convencionais da fisioterapia e os testes funcionais com poder preditivo sobre as medidas genéricas e de condição específica do estado de saúde. RESULTADOS/DISCUSSÃO: O Timed Up & Go Test combinado com o teste de subir escadas explicou 36% na percepção do WOMAC função, o teste de subir e descer escada combinado com a estatura explicaram 34,2% do MOS-SF-36 na dimensão desempenho físico. CONCLUSÃO: Das medidas de resultados abordadas, o Timed Up & Go Test o teste de descer escadas foram os que melhor estimaram a percepção da função do joelho. É recomendada a utilização destes testes na investigação dos resultados em fisioterapia em OA joelho