Uniform Recovery Research Articles

Uniform Recovery Guarantees for Quantized Corrupted Sensing Using Structured or Generative Priors

Uniform Recovery Guarantees for Quantized Corrupted Sensing Using Structured or Generative Priors

Quantizing Heavy-Tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recovery

Quantizing Heavy-Tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recovery

Comparison of QuEChERS and Liquid–Liquid extraction methods for the simultaneous analysis of pesticide residues using LC-MS/MS

In 2004, the Food Code of Korea adopted a multi-class multi-residue pesticide analysis method, which employed liquid–liquid extraction (LLE) and solid-phase extraction for sample purification. After several modifications, the LLE stage was replaced by the QuEChERS method in October 2021. Thus, in the current study a comparison was carried out between the new QuEChERS method and the conventional LLE method for the simultaneous analysis of multiple pesticide residues. More specifically, 275 pesticide compounds were measured in spinach, rice, and mandarin matrices using LC-MS/MS, and the linearity, LOD, LOQ, recovery, and matrix effect were determined. Following both the QuEChERS and LLE, the matrix-matched calibration curve plotted using the extracts of blank matrix extracts showed that the majority of pesticides exhibited a highly linear relationship, with coefficients of determination >0.99. In addition, the LOD was 0.00003–0.004 mg/kg, and the LOQ was 0.0001–0.01 mg/kg. For the different matrices, the average recovery of the QuEChERS method was 101.3–105.8%, while that of the LLE method was 62.6–85.5%. Due to the fact that the LLE and QuEChERS methods exhibited a tendency of suppression for the various matrices examined, matrix-matched calibration was required during quantification. Indeed, introduction of the QuEChERS method allowed matrix-matched calibration to be conducted during quantification, while the previously employed LLE method did not involve such processes. These changes therefore resulted in a more accurate quantification in addition to a reduced experimental time and cost. • We compared QuEChERS to LLE in multi-residue analysis in foods by LC-MS/MS. • QuEChERS has higher and more uniform recovery rates among matrices than LLE. • Both methods require matrix-matched calibration owing to ion suppression. • QuEChERS and matrix-matched calibration improve quantification accuracy.

A Unified Approach to Uniform Signal Recovery From Nonlinear Observations

Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong nonlinear distortions in the observation process. An important characteristic of associated guarantees is uniformity, i.e., recovery succeeds for an entire class of structured signals with a fixed measurement ensemble. However, despite significant results in various special cases, a general understanding of uniform recovery from nonlinear observations is still missing. This paper develops a unified approach to this problem under the assumption of i.i.d. sub-Gaussian measurement vectors. Our main result shows that a simple least-squares estimator with any convex constraint can serve as a universal recovery strategy, which is outlier robust and does not require explicit knowledge of the underlying nonlinearity. Based on empirical process theory, a key technical novelty is an approximative increment condition that can be implemented for all common types of nonlinear models. This flexibility allows us to apply our approach to a variety of problems in nonlinear compressed sensing and high-dimensional statistics, leading to several new and improved guarantees. Each of these applications is accompanied by a conceptually simple and systematic proof, which does not rely on any deeper properties of the observation model. On the other hand, known local stability properties can be incorporated into our framework in a plug-and-play manner, thereby implying near-optimal error bounds.

Dictionary-sparse recovery from heavy-tailed measurements

Abstract The recovery of signals that are sparse not in a given basis, but rather sparse with respect to an over-complete dictionary is one of the most flexible settings in the field of compressed sensing with numerous applications. As in the standard compressed sensing setting, it is possible that the signal can be reconstructed efficiently from a few linear measurements, for example, by the so-called $\ell _1$-synthesis method. However, it has been less well understood which measurement matrices provably work for this setting. Whereas in the standard setting, it has been shown that even certain heavy-tailed measurement matrices can be used in the same sample complexity regime as Gaussian matrices, comparable results are only available for the restrictive class of sub-Gaussian measurement matrices as far as the recovery of dictionary-sparse signals via $\ell _1$-synthesis is concerned. In this work, we fill this gap and establish optimal guarantees for the recovery of vectors that are (approximately) sparse with respect to a dictionary via the $\ell _1$-synthesis method from linear, potentially noisy measurements for a large class of random measurement matrices. In particular, we show that random measurements that fulfill only a small-ball assumption and a weak moment assumption, such as random vectors with i.i.d. Student-$t$ entries with a logarithmic number of degrees of freedom, lead to comparable guarantees as (sub-)Gaussian measurements. Our results apply for a large class of both random and deterministic dictionaries. As a technical tool, we show a bound on the expectation of the sum of squared order statistics under very general assumptions, which might be of independent interest. As a corollary of our results, we also obtain a slight improvement on the weakest assumption on a measurement matrix with i.i.d. rows sufficient for uniform recovery in standard compressed sensing, improving on results by Lecué and Mendelson and by Dirksen, Lecué and Rauhut.

Analysis of sparse recovery for Legendre expansions using envelope bound

We provide novel sufficient conditions for the uniform recovery of sparse Legendre expansions using ℓ1 minimization, where the sampling points are drawn according to orthogonalization (uniform) measure. So far, conditions of the form m ≳ Θ 2 s × log factors have been relied on to determine the minimum number of samples m that guarantees successful reconstruction of s-sparse vectors when the measurement matrix is associated to an orthonormal system. However, in case of sparse Legendre expansions, the uniform bound Θ of Legendre systems is so high that these conditions are unable to provide meaningful guarantees. In this paper, we present an analysis which employs the envelop bound of all Legendre polynomials instead, and prove a new recovery guarantee for s-sparse Legendre expansions, m ≳ s 2 × log factors , which is independent of Θ. Arguably, this is the first recovery condition established for orthonormal systems without assuming the uniform boundedness of the sampling matrix. The key ingredient of our analysis is an extension of chaining arguments, recently developed in Bourgain and Chkifa et al., to handle the envelope bound. Furthermore, our recovery condition is proved via restricted eigenvalue property, a less demanding replacement of restricted isometry property which is perfectly suited to the considered scenario. Along the way, we derive simple criteria to detect good sample sets. Our numerical tests show that sets of uniformly sampled points that meet these criteria will perform better recovery on average.

Взаємозв’язок патофізіологічних процесів, що відбуваються в плевральній порожнині при згорнутому гемотораксі та аутогемоплевродезі

Актуальність. Незважаючи на широке впровадження в торакальну хірургію малоінвазивних методів резекції, плевродез залишається у ряді випадків єдиним визначальним методом радикальної хірургічної корекції. Особливо яскраво це проявляється при операціях у хворих із поширеними формами бульозної емфіземи легенів. У той же час існуючі види плевродезу викликають серйозні супутні ускладнення. З урахуванням цього був розроблений метод аутогемоплевродезу, заснований на патофізіології процесів, що виникають у плевральній порожнині після попадання в неї крові, в основу якого були покладені процеси, характерні для розвитку і перетворення згорнутого гемотораксу. Метою дослідження стало вивчення патофізіології плевральної порожнини при штучному створенні в ній гемотораксу. Матеріали та методи. Контрольну групу склали 36 хворих, у яких гемоторакс був викликаний проникаючими колото-різаними пораненнями грудної клітки. Із них у 21 пацієнта відзначався малий або середній гемоторакс, у 15 хворих у зв’язку зі згорнутим гемотораксом була виконана його ВТС-евакуація. Основну групу склали 40 хворих, у яких гемоторакс виникав унаслідок виконання їм ВТС-резекції легені і плевродезу з приводу бульозної емфіземи, з них у 24 був виконаний коагуляційний східчастий плевродез, у 16 — аутогемоплевродез за розробленою методикою. Як основний показник, що відображає процеси формування фібрину і фібринолізу в плевральній порожнині, досліджувався плазміноген, відсоток активності якого визначався в сироватці крові і плевральному ексудаті триразово: через 1 годину і 24 години після операції, а також на 5-ту післяопераційну добу. Результати. У перші години після операції відбувалося зниження рівня плазміногену крові в усіх хворих, окрім тих, яким була виконана ВТС-резекція зі східчастим плевродезом. Через добу після операції в групі хворих із малим і середнім гемотораксом розпочиналося повільне відновлення рівня плазміногену, через 5 діб його концентрація в крові повністю відновлювалася. У пацієнтів, що перенесли евакуацію згорнутого гемотораксу, через 1 годину після операції відзначалося стандартне зниження плазміногену. На 5-ту добу рівень плазміногену в крові відновився тільки наполовину. Такі ж значення плазміногену в часових проміжках 1 година та 5 діб були в групі хворих, яким після ВТС-резекції був виконаний аутогемоплевродез, а через 24 години після аутогемоплевродезу вже починалося відновлення рівня плазміногену. У плевральному ексудаті відзначалося помірне зниження плазміногену в пацієнтів, що перенесли ВТС-резекцію зі східчастим плевродезом і ПХО з дренуванням плевральної порожнини через 1 годину після операції, та потім його рівномірне відновлення до 5-ї доби. У хворих зі згорнутим гемотораксом було більш глибоке падіння рівня плазміногену через 1 годину після операції і рівномірне, але не остаточне його відновлення до 5-ї доби. Аутогемоплевродез призводив до різкого зниження плазміногену в плевральному ексудаті через 1 годину після операції, та його рівень не виріс до 5-ї доби. Висновки. Зниження плазміногену в плевральному ексудаті стало прямим відображенням виснажуючої дії аутокрові. Аутогемоплевродез є втручанням, що моделює процеси, які відбуваються в плевральній порожнині при згорнутому гемотораксі в більш м’якому варіанті; при ньому відбувається пригнічення лікворного фібринолізу, аналогічне такому при згорнутому гемотораксі.

India’s food supply chain during the pandemic

We document the impact of India’s COVID-19 lockdown on the food supply chain. Food arrivals in wholesale markets dropped by 69% in the three weeks following the lockdown and wholesale prices rose by 8%. Six weeks after the lockdown began, volumes and prices had fully recovered. The initial food supply shock was highly correlated with early incidence of COVID-19. We provide evidence that this correlation is due more to state-level lockdown policy variation than local responses of those in the food supply chain. Finally, during the recovery phase, the correlation between the food supply disruption and COVID-19 exposure disappeared, suggesting uniform recovery.

Analysis of the ratio of ℓ1 and ℓ2 norms in compressed sensing

We study the ratio of ℓ1 and ℓ2 norms (ℓ1/ℓ2) as a sparsity-promoting objective in compressed sensing. We first propose a novel criterion that guarantees that an s-sparse signal is the local minimizer of the ℓ1/ℓ2 objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is satisfied for a class of random matrices. We also present analysis on the robustness of the procedure when noise pollutes data. Numerical experiments are provided that compare ℓ1/ℓ2 with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach support selection, and we demonstrate that it empirically improves the performance of existing ℓ1/ℓ2 algorithms.

The challenges of rehabilitation after COVID-19

Due to the outbreak of the COVID-19 pandemic, social life and the clinical state of change of state. This disease is caused by the SARS-CoV-2 virus and is characterized by high infectivity and mortality. Due to the diversity of the tested tests, it will be difficult to obtain uniform characteristics, resulting in a uniform recovery plan for each patient. Rehabilitation, repair, execution, restoration to health, independence and reduction in value due to COVID-19.

Efficient iterative thresholding algorithms with functional feedbacks and null space tuning

An accelerated class of adaptive scheme of iterative thresholding algorithms is studied analytically and empirically. They are based on the feedback mechanism of the null space tuning techniques. The main contribution of this article is the accelerated convergence analysis and proofs with a variable/adaptive index selection and different feedback principles at each iteration. The convergence analysis requires no longer a priori sparsity information s of a signal. It is shown that uniform recovery of all s-sparse signals from given linear measurements can be achieved under reasonable (preconditioned) restricted isometry conditions. Accelerated convergence rate and improved convergence conditions are obtained by selecting an appropriate size of the index support per iteration. The theoretical findings are sufficiently demonstrated and confirmed by extensive numerical experiments. It is also observed that the proposed algorithms have a clearly advantageous balance of efficiency, adaptivity and accuracy compared with all other state-of-the-art greedy iterative algorithms.

Compressed Sensing with 1D Total Variation: Breaking Sample Complexity Barriers via Non-Uniform Recovery

AbstractThis paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform recovery of all $s$-gradient-sparse signals in ${\mathbb{R}}^n$ is only possible with $m \gtrsim \sqrt{s n} \cdot{\operatorname{PolyLog}}(n)$ measurements. Such a condition is especially prohibitive for high-dimensional problems, where $s$ is much smaller than $n$. However, previous empirical findings seem to indicate that this sampling rate does not reflect the typical behavior of total variation minimization. The present work provides a rigorous analysis that breaks the $\sqrt{s n}$-bottleneck for a large class of “natural” signals. The main result shows that non-uniform recovery succeeds with high probability for $m \gtrsim s \cdot{\operatorname{PolyLog}}(n)$ measurements if the jump discontinuities of the signal vector are sufficiently well separated. In particular, this guarantee allows for signals arising from a discretization of piecewise constant functions defined on an interval. The key ingredient of the proof is a novel upper bound for the associated conic Gaussian mean width, which is based on a signal-dependent, non-dyadic Haar wavelet transform. Furthermore, a natural extension to stable and robust recovery is addressed.

Uniform recovery in infinite-dimensional compressed sensing and applications to structured binary sampling

Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world inverse problems, which are typically modeled in infinite-dimensional spaces, and where the application of finite-dimensional approaches can lead to noticeable artefacts. Another typical feature of such problems is that the signals are not only sparse in some dictionary, but possess a so-called local sparsity in levels structure. Consequently, the sampling scheme should be designed so as to exploit this additional structure. In this paper, we introduce a series of uniform recovery guarantees for infinite-dimensional compressed sensing based on sparsity in levels and so-called multilevel random subsampling. By using a weighted ℓ 1 -regularizer we derive measurement conditions that are sharp up to log factors, in the sense that they agree with the best known measurement conditions for oracle estimators in which the support is known a priori. These guarantees also apply in finite dimensions, and improve existing results for unweighted ℓ 1 -regularization. To illustrate our results, we consider the problem of binary sampling with the Walsh transform using orthogonal wavelets. Binary sampling is an important mechanism for certain imaging modalities. Through carefully estimating the local coherence between the Walsh and wavelet bases, we derive the first known recovery guarantees for this problem.

The Benefits of Acting Locally: Reconstruction Algorithms for Sparse in Levels Signals With Stable and Robust Recovery Guarantees

The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel acquisition, radar, and the sparse corruptions problem. Reconstruction strategies for sparse in levels signals usually rely on a suitable convex optimization program. Notably, although iterative and greedy algorithms can outperform convex optimization in terms of computational efficiency and have been studied extensively in the case of standard sparsity, little is known about their generalizations to the sparse in levels setting. In this paper, we bridge this gap by showing new stable and robust uniform recovery guarantees for sparse in level variants of the iterative hard thresholding and the CoSaMP algorithms. Our theoretical analysis generalizes recovery guarantees currently available in the case of standard sparsity and favorably compare to sparse in levels guarantees for weighted $\ell^1$ minimization. In addition, we also propose and numerically test an extension of the orthogonal matching pursuit algorithm for sparse in levels signals.

Improved Recovery Guarantees and Sampling Strategies for TV Minimization in Compressive Imaging

In this paper, we consider the use of total variation (TV) minimization for compressive imaging, that is, image reconstruction from subsampled measurements. Focusing on two important imaging modalities---namely, Fourier imaging and structured binary imaging via the Walsh--Hadamard transform---we derive uniform recovery guarantees asserting stable and robust recovery for arbitrary random sampling strategies. Using this, we then derive a class of sampling strategies which are theoretically near-optimal for recovery of approximately gradient-sparse images. For Fourier sampling, we show recovery of such an image from $m \gtrsim_d s \cdot \log^2(s) \cdot \log^4(N)$ measurements, in $d \geq 1$ dimensions. When $d = 2$, this improves the current state-of-the-art result by a factor of $\log(s) \cdot \log(N)$. It also extends it to arbitrary dimensions $d \geq 2$. For Walsh sampling, we prove that $m \gtrsim_d s \cdot \log^2(s) \cdot \log^2(N/s) \cdot \log^3(N) $ measurements suffice in $d \geq 2$ dimensions. To the best of our knowledge, this is the first recovery guarantee for structured binary sampling with TV minimization.

India’s Food Supply Chain during the Pandemic

We document the impact of India’s COVID-19 lockdown on the food supply chain. Food arrivals in wholesale markets dropped by 69% in the three weeks following the lockdown and wholesale prices rose by 8%. Six weeks after the lockdown began, volumes and prices had fully recovered. The initial food supply shock was highly correlated with early incidence of COVID-19. We provide evidence that this correlation is due more to state-level lockdown policy variation than local responses of those in the food supply chain. Finally, during the recovery phase, the correlation between the food supply disruption and COVID-19 exposure disappeared, suggesting uniform recovery.

Statistical Considerations for Drawing Conclusions About Recovery

Background Numerous studies have found associations when change scores are regressed onto initial impairments in people with stroke (slopes ≈ 0.7). However, there are important statistical considerations that limit the conclusions we can draw about recovery from these studies. Objective To provide an accessible checklist of conceptual and analytical issues on longitudinal measures of stroke recovery. Proportional recovery is an illustrative example, but these considerations apply broadly to studies of change over time. Methods Using a pooled data set of n = 373 Fugl-Meyer Assessment upper extremity scores, we ran simulations to illustrate 3 considerations: (1) how change scores can be problematic in this context; (2) how “nil” and nonzero null-hypothesis significance tests can be used; and (3) how scale boundaries can create the illusion of proportionality, whereas other analytical procedures (eg, post hoc classifications) can augment this problem. Results Our simulations highlight several limitations of common methods for analyzing recovery. We find that uniform recovery leads to similar group-level statistics (regression slopes) and individual-level classifications (into fitters and nonfitters) that have been claimed as evidence for the proportional recovery rule. New analyses, however, also speak to the complexities in variance about the regression slope. Conclusions Our results highlight that one cannot identify whether proportional recovery is true or not based on commonly used methods. We illustrate how these techniques, measurement tools, and post hoc classifications (eg, nonfitters) can create spurious results. Going forward, the field needs to carefully consider the influence of these factors on how we measure, analyze, and conceptualize recovery.

Production of 7-methylxanthine from Theobromine by Metabolically Engineered E. coli

In this work, a novel biocatalytic process for the production of 7-methylxanthines from theobromine, an economic feedstock has been developed. Bench scale production of 7-methlxanthine has been demonstrated. The biocatalytic process used in this work operates at 30 OC and atmospheric pressure, and is environmentally friendly. The biocatalyst was E. coli BL21(DE3) engineered with ndmB/D genes combinations. These modifications enabled specific N7- demethylation of theobromine to 7-methylxanthine. This production process consists of uniform fermentation conditions with a specific metabolically engineered strain, uniform induction of specific enzymes for 7-methylxanthine production, uniform recovery and preparation of biocatalyst for reaction and uniform recovery of pure 7-methylxanthine.
 Many E. coli BL21(DE3) strains metabolically engineered with single and/or multiple ndmB/D genes were tested for catalytic activity, and the best strains which had the higher activity were chosen to carry out the N-demethylation reaction of theobromine. Strain pBD2dDB had the highest activity for the production of 7-methylxanthine from theobromine. That strain was used to find the optimum amount of cells required to achieve complete conversion of theobromine to 7-methylxanthine within two hours. It was found that the optimum concentration of pBD2dDB strain to achieve 100% conversion of 0.5 mM theobromine to 7-methylxanthine was 5 mg/mL. The cell growth of pBD2dDB strain was studied using two different growth media, (Luria-Bertani Broth and Super Broth). Super broth was found to be the best medium to produce the highest amount of cell paste (1.5 g). Subsequently, the process was scaled up in which 2 L reaction volume was used to produce 7-methylxanthine (100% conversion) from 0.5 mM theobromine catalyzed by pBD2dDB strain. The reactions was carried out at 30 oC and 250 rpm shaker speed, and the reaction medium was 50 mM potassium phosphate buffer (pH=7). 7-methylxanthines was separated by preparative chromatography with high recovery, and the product solution was collected, purified by drying at 120-140 oC for 4 hours and, recovered (127 mg). Purity of the isolated 7-methylxanthine was comparable to authentic standards with no contaminant peaks, as observed by HPLC, LC-MS, and NMR.

Block-sparse recovery of semidefinite systems and generalized null space conditions

This article considers the recovery of low-rank matrices via a convex nuclear-norm minimization problem and presents two null space properties (NSP) which characterize uniform recovery for the case of block-diagonal matrices and block-diagonal positive semidefinite matrices. These null-space conditions turn out to be special cases of a new general setup, which allows to derive the mentioned NSPs and well-known NSPs from the literature. We discuss the relative strength of these conditions and also present a deterministic class of matrices that satisfies the block-diagonal semidefinite NSP.

Estimation of the Mechanical Recovery Potential of Spilled Oil at Sea Considering the Spatial Thickness Distribution

Recovery modeling and countermeasures for oil spilled at sea have been extensively researched, but research remains insufficient on recovery potential estimation methods. It is required to access the mechanical recovery potential by considering the relationship between oil behavior, environmental conditions, and the performance of clean-up activities. Two response-planning models were developed in this study. One is a spatially uniform recovery model for estimating recovery potential that reflects weathering, oil properties, and equipment efficiency. The other is a spatially nonuniform recovery model that considers not only the above characteristics but also local thickness reduction by skimming. A comparison between the two models and an analysis of their effects on response was carried out through the calculation using an accident scenario. It is possible to analyze the effect of the thin slicks, natural dissipation, and the quantification of deployable skimming systems with the spatially nonuniform recovery model. Finally, we analyzed interrelationships among residual oil volume on the sea, response time, and the number of skimming systems.