A new perspective on the Propagation-Separation approach: Taking advantage of the propagation condition

The Propagation-Separation approach is an iterative procedure for pointwise estimation of local constant and local polynomial functions. The estimator is defined as a weighted mean of the observations with data-driven weights. Within homogeneous regions it ensures a similar behavior as non-adaptive smoothing (propagation), while avoiding smoothing among distinct regions (separation). In order to enable a proof of stability of estimates, the authors of the original study introduced an additional memory step aggregating the estimators of the successive iteration steps. Here, we study theoretical properties of the simplified algorithm, where the memory step is omitted. In particular, we introduce a new strategy for the choice of the adaptation parameter yielding propagation and stability for local constant functions with sharp discontinuities.Comment: 28 pages, 5 figure

The Propagation-Separation Approach: Consequences of model misspecification

The article presents new results on the Propagation-Separation Approach by Polzehl and Spokoiny (2006). This iterative procedure provides a unified approach for nonparametric estimation, supposing a local parametric model. The adaptivity of the estimator ensures sensitivity to structural changes. Originally, an additional memory step was included into the algorithm, where most of the theoretical properties were based on. However, in practice, a simplified version of the algorithm is used, where the memory step is omitted. Hence, we aim to justify this simplified procedure by means of a theoretical study and numerical simulations. In our previous study, we analyzed the simplified Propagation-Separation Approach, supposing piecewise constant parameter functions with sharp discontinuities. Here, we consider the case of a misspecified model

The Propagation-Separation Approach

Lokal parametrische Modelle werden häufig im Kontext der nichtparametrischen Schätzung verwendet. Bei einer punktweisen Schätzung der Zielfunktion können die parametrischen Umgebungen mithilfe von Gewichten beschrieben werden, die entweder von den Designpunkten oder (zusätzlich) von den Beobachtungen abhängen. Der Vergleich von verrauschten Beobachtungen in einzelnen Punkten leidet allerdings unter einem Mangel an Robustheit. Der Propagations-Separations-Ansatz von Polzehl und Spokoiny [2006] verwendet daher einen Multiskalen-Ansatz mit iterativ aktualisierten Gewichten. Wir präsentieren hier eine theoretische Studie und numerische Resultate, die ein besseres Verständnis des Verfahrens ermöglichen. Zu diesem Zweck definieren und untersuchen wir eine neue Strategie für die Wahl des entscheidenden Parameters des Verfahrens, der Adaptationsbandweite. Insbesondere untersuchen wir ihre Variabilität in Abhängigkeit von der unbekannten Zielfunktion. Unsere Resultate rechtfertigen eine Wahl, die unabhängig von den jeweils vorliegenden Beobachtungen ist. Die neue Parameterwahl liefert für stückweise konstante und stückweise beschränkte Funktionen theoretische Beweise der Haupteigenschaften des Algorithmus. Für den Fall eines falsch spezifizierten Modells führen wir eine spezielle Stufenfunktion ein und weisen eine punktweise Fehlerschranke im Vergleich zum Schätzer des Algorithmus nach. Des Weiteren entwickeln wir eine neue Methode zur Entrauschung von diffusionsgewichteten Magnetresonanzdaten. Unser neues Verfahren (ms)POAS basiert auf einer speziellen Beschreibung der Daten, die eine zeitgleiche Glättung bezüglich der gemessenen Positionen und der Richtungen der verwendeten Diffusionsgradienten ermöglicht. Für den kombinierten Messraum schlagen wir zwei Distanzfunktionen vor, deren Eignung wir mithilfe eines differentialgeometrischen Ansatzes nachweisen. Schließlich demonstrieren wir das große Potential von (ms)POAS auf simulierten und experimentellen Daten.In statistics, nonparametric estimation is often based on local parametric modeling. For pointwise estimation of the target function, the parametric neighborhoods can be described by weights that depend on design points or on observations. As it turned out, the comparison of noisy observations at single points suffers from a lack of robustness. The Propagation-Separation Approach by Polzehl and Spokoiny [2006] overcomes this problem by using a multiscale approach with iteratively updated weights. The method has been successfully applied to a large variety of statistical problems. Here, we present a theoretical study and numerical results, which provide a better understanding of this versatile procedure. For this purpose, we introduce and analyse a novel strategy for the choice of the crucial parameter of the algorithm, namely the adaptation bandwidth. In particular, we study its variability with respect to the unknown target function. This justifies a choice independent of the data at hand. For piecewise constant and piecewise bounded functions, this choice enables theoretical proofs of the main heuristic properties of the algorithm. Additionally, we consider the case of a misspecified model. Here, we introduce a specific step function, and we establish a pointwise error bound between this function and the corresponding estimates of the Propagation-Separation Approach. Finally, we develop a method for the denoising of diffusion-weighted magnetic resonance data, which is based on the Propagation-Separation Approach. Our new procedure, called (ms)POAS, relies on a specific description of the data, which enables simultaneous smoothing in the measured positions and with respect to the directions of the applied diffusion-weighting magnetic field gradients. We define and justify two distance functions on the combined measurement space, where we follow a differential geometric approach. We demonstrate the capability of (ms)POAS on simulated and experimental data

Targeted mutagenesis of the Sap47 gene of Drosophila: Flies lacking the synapse associated protein of 47 kDa are viable and fertile

BACKGROUND: Conserved proteins preferentially expressed in synaptic terminals of the nervous system are likely to play a significant role in brain function. We have previously identified and molecularly characterized the Sap47 gene which codes for a novel synapse associated protein of 47 kDa in Drosophila. Sequence comparison identifies homologous proteins in numerous species including C. elegans, fish, mouse and human. First hints as to the function of this novel protein family can be obtained by generating mutants for the Sap47 gene in Drosophila. RESULTS: Attempts to eliminate the Sap47 gene through targeted mutagenesis by homologous recombination were unsuccessful. However, several mutants were generated by transposon remobilization after an appropriate insertion line had become available from the Drosophila P-element screen of the Bellen/Hoskins/Rubin/Spradling labs. Characterization of various deletions in the Sap47 gene due to imprecise excision of the P-element identified three null mutants and three hypomorphic mutants. Null mutants are viable and fertile and show no gross structural or obvious behavioural deficits. For cell-specific over-expression and "rescue" of the knock-out flies a transgenic line was generated which expresses the most abundant transcript under the control of the yeast enhancer UAS. In addition, knock-down of the Sap47 gene was achieved by generating 31 transgenic lines expressing Sap47 RNAi constructs, again under UAS control. When driven by a ubiquitously expressed yeast transcription factor (GAL4), Sap47 gene suppression in several of these lines is highly efficient resulting in residual SAP47 protein concentrations in heads as low as 6% of wild type levels. CONCLUSION: The conserved synaptic protein SAP47 of Drosophila is not essential for basic synaptic function. The Sap47 gene region may be refractory to targeted mutagenesis by homologous recombination. RNAi using a construct linking genomic DNA to anti-sense cDNA in our hands is not more effective than using a cDNA-anti-sense cDNA construct. The tools developed in this study will now allow a detailed analysis of the molecular, cellular and systemic function of the SAP47 protein in Drosophila

Doubling your payoff: winning pain relief engages endogenous pain inhibition

When in pain, pain relief is much sought after, particularly for individuals with chronic pain. In analogy to augmentation of the hedonic experience (“liking”) of a reward by the motivation to obtain a reward (“wanting”), the seeking of pain relief in a motivated state might increase the experience of pain relief when obtained. We tested this hypothesis in a psychophysical experiment in healthy human subjects, by assessing potential pain-inhibitory effects of pain relief “won” in a wheel of fortune game compared with pain relief without winning, exploiting the fact that the mere chance of winning induces a motivated state. The results show pain-inhibitory effects of pain relief obtained by winning in behaviorally assessed pain perception and ratings of pain intensity. Further, the higher participants scored on the personality trait novelty seeking, the more pain inhibition was induced. These results provide evidence that pain relief, when obtained in a motivated state, engages endogenous pain-inhibitory systems beyond the pain reduction that underlies the relief in the first place. Consequently, such pain relief might be used to improve behavioral pain therapy, inducing a positive, perhaps self-amplifying feedback loop of reduced pain and improved functionality

Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS

In this article we present a noise reduction method (msPOAS) for multi-shell diffusionweighted magnetic resonance data. To our knowledge, this is the first smoothing method which allows simultaneous smoothing of all q-shells. It is applied directly to the diffusion weighted data and consequently allows subsequent analysis by any model. Due to its adaptivity, the procedure avoids blurring of the inherent structures and preserves discontinuities. MsPOAS extends the recently developed positionorientation adaptive smoothing (POAS) procedure to multi-shell experiments. At the same time it considerably simplifies and accelerates the calculations. The behavior of the algorithm msPOAS is evaluated on diffusion-weighted data measured on a single shell and on multiple shells

Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS

In this article we present a noise reduction method (msPOAS) for multi-shell diffusion-weighted magnetic resonance data. To our knowledge, this is the first smoothing method which allows simultaneous smoothing of all q-shells. It is applied directly to the diffusion weighted data and consequently allows subsequent analysis by any model. Due to its adaptivity, the procedure avoids blurring of the inherent structures and preserves discontinuities. MsPOAS extends the recently developed position-orientation adaptive smoothing (POAS) procedure to multi-shell experiments. At the same time it considerably simplifies and accelerates the calculations. The behavior of the algorithm msPOAS is evaluated on diffusion-weighted data measured on a single shell and on multiple shells

Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS

In this article we present a noise reduction method (msPOAS) for multi-shell diffusion-weighted magnetic resonance data. To our knowledge, this is the first smoothing method which allows simultaneous smoothing of all q-shells. It is applied directly to the diffusion weighted data and consequently allows subsequent analysis by any model. Due to its adaptivity, the procedure avoids blurring of the inherent structures and preserves discontinuities. MsPOAS extends the recently developed position-orientation adaptive smoothing (POAS) procedure to multi-shell experiments. At the same time it considerably simplifies and accelerates the calculations. The behavior of the algorithm msPOAS is evaluated on diffusion-weighted data measured on a single shell and on multiple shells

Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS)

We introduce an algorithm for diffusion weighted magnetic resonance imaging data enhancement based on structural adaptive smoothing in both space and diffusion direction. The method, called POAS, does not refer to a specific model for the data, like the diffusion tensor or higher order models. It works by embedding the measurement space into a space with defined metric and group operations, in this case the Lie group of three-dimensional Euclidean motion SE(3). Subsequently, pairwise comparisons of the values of the diffusion weighted signal are used for adaptation. The position-orientation adaptive smoothing preserves the edges of the observed fine and anisotropic structures. The POAS-algorithm is designed to reduce noise directly in the diffusion weighted images and consequently also to reduce bias and variability of quantities derived from the data for specific models. We evaluate the algorithm on simulated and experimental data and demonstrate that it can be used to reduce the number of applied diffusion gradients and hence acquisition time while achieving similar quality of data, or to improve the quality of data acquired in a clinically feasible scan time setting

Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS)

We introduce an algorithm for diffusion weighted magnetic resonance imaging data enhancement based on structural adaptive smoothing in both space and diffusion direction. The method, called POAS, does not refer to a specific model for the data, like the diffusion tensor or higher order models. It works by embedding the measurement space into a space with defined metric and group operations, in this case the Lie group of three-dimensional Euclidean motion SE(3). Subsequently, pairwise comparisons of the values of the diffusion weighted signal are used for adaptation. The position-orientation adaptive smoothing preserves the edges of the observed fine and anisotropic structures. The POAS-algorithm is designed to reduce noise directly in the diffusion weighted images and consequently also to reduce bias and variability of quantities derived from the data for specific models. We evaluate the algorithm on simulated and experimental data and demonstrate that it can be used to reduce the number of applied diffusion gradients and hence acquisition time while achieving similar quality of data, or to improve the quality of data acquired in a clinically feasible scan time setting