Total Variation as a local filter

International audienceIn the Rudin-Osher-Fatemi (ROF) image denoising model, Total Variation (TV) is used as a global regularization term. However, as we observe, the local interactions induced by Total Variation do not propagate much at long distances in practice, so that the ROF model is not far from being a local filter. In this paper, we propose to build a purely local filter by considering the ROF model in a given neighborhood of each pixel. We show that appropriate weights are required to avoid aliasing-like effects, and we provide an explicit convergence criterion for an associated dual minimization algorithm based on Chambolle's work. We study theoretical properties of the obtained local filter, and show that this localization of the ROF model brings an interesting optimization of the bias-variance trade-off, and a strong reduction a ROF drawback called "staircasing effect". We finally present a new denoising algorithm, TV-means, that efficiently combines the idea of local TV-filtering with the non-local means patch-based method

Inter-frequency Bias Estimation for the GPS Monitor Station Network

The inter-frequency bias (IFB) is present in all dual frequency combinations of GPS pseudorange and carrier phase observables. It is caused by the path dependent signal delays in both the satellite and receiver. That delay can be directly measured for a space vehicle prior to launch, or for a ground based receiver prior to its being used in the field. However the bias is known to drift, and monitoring the delay estimate by direct measurement is time consuming for ground based receivers and impossible for deployed space vehicles. Hansen (2002) examined the observability of IFB through a global model of ionosphere total electron content (TEC). Variation in the receiver portion of the IFB can also be observed in receivers with antennae in a zero-baseline configuration. This is referred to as an inter-receiver bias (IRB). In this study a Kalman filter is formulated to observe IFBs and IRBs. Process noise is used to allow the filter to track changes in the IFBs and IRBs. The filter also implements constraints to reflect the fact that a given IRB is not linearly independent of the IFBs. Because the receivers are distributed on a global scale, the Kalman filter requires a globally observable phenomenon by which to tie the IFBs. In this case ionosphere delay provides such a phenomenon. The filter was applied to observations collected by GPS monitor stations that comprise the National Geospatial- Intelligence Agency Monitor Station Network (MSN). Each monitor station contains two geodetic quality receivers in a zero-baseline configuration and continuously collects GPS observations. The GPS observations collected by this network are used to produce both precise ephemeris and the broadcast ephemeris. GPS observations made through the network are incorporated into the GPS Master Control Station (MCS) Kalman filter of the Operational Control System (OCS) (Wiley, 2006). The Kalman filter in the OCS estimates the orbital parameters that are transmitted via the navigation message. If estimated effectively, knowledge of the receiver portion of the IFB can aid in achieving better ionosphere models. IFBs are made observable using a global ionosphere delay model. A ninth order spherical harmonic model derived by Y.C. Chao (1997) was used in this study for ionosphere delay. Chao used this spherical harmonic model to capture ionospheric variations that occurred over a smaller global region in his IFB estimation process. In this study a similar model was used but was verified using observations that span a global coverage. The receiver portion of the IFB is observed precisely using the IRB. In this study error terms were introduced into the Kalman filter design to realign the IRB estimates to the IFB estimates produced for each of the two receivers in a zero baseline configuration. For a nominal epoch of measurement, there were 198 noisy measurements used each epoch to generate twelve monitor station specific IRBs. The IRB estimates showed small, decimeter level dynamic variation over the period of a day. The quality of the IFB estimate directly affects the quality of the ionospheric model formed during the estimation process. Results verify that the filter is operating properly. The ionosphere model, though simple, demonstrates that the total electron content (TEC) peaks during local noon and is at a minimum during local night. IRB estimates are roughly constant over time and have a magnitude of less than 2.5 meters. Similar estimates are formed for the IFBs, however when processing one day of observations, the IFB estimates are less stable than those of the IRBs. Future effort will involve tuning the filter, and establishing criteria for its convergence

Enhancement of Historical Printed Document Images by Combining Total Variation Regularization and Non-Local Means Filtering

This paper proposes a novel method for document enhancement which combines two recent powerful noise-reduction steps. The first step is based on the total variation framework. It flattens background grey-levels and produces an intermediate image where background noise is considerably reduced. This image is used as a mask to produce an image with a cleaner background while keeping character details. The second step is applied to the cleaner image and consists of a filter based on non-local means: character edges are smoothed by searching for similar patch images in pixel neighborhoods. The document images to be enhanced are real historical printed documents from several periods which include several defects in their background and on character edges. These defects result from scanning, paper aging and bleed- through. The proposed method enhances document images by combining the total variation and the non-local means techniques in order to improve OCR recognition. The method is shown to be more powerful than when these techniques are used alone and than other enhancement methods

Implementation of composite semijoins using a variation of Bloom filters.

Different from a centralized database system, distributed query processing involves data transmission among different sites and this communication cost is a dominant factor compared to local processing cost. So, the objective of distributed query optimization is to find strategies to minimize the amount of data transmitted over the network. Since optimal query processing in distributed database systems has been shown to be an NP-hard problem, heuristics are applied to find a near-optimal processing strategy. Previous research has mainly focused on the use of joins, semijoins, and hash semijoins (Bloom filters). The semijoin is a commonly recognized operator, which provides efficient query results. As a variation of semijoin, the composite semijoin is beneficial to do semijoins as one composite rather than as multiple single column semijoins. The Hash semijoin (which uses a Bloom filter) is used to minimize the cost of a semijoin operation. This thesis report provides a summary of each category of query processing techniques and optimization algorithms. Also in this thesis, we propose a new algorithm called Composite Semijoin Filter by combining the idea of composite semijoins, Bloom filters and PERF joins. One of the advantages of this algorithm is to avoid collisions. The algorithm is evaluated and compared with initial feasible solution (IFS) and another filter-based algorithm. It has been shown that the algorithm gives substantial reduction on relations and the total cost.Dept. of Computer Science. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .Z58. Source: Masters Abstracts International, Volume: 43-01, page: 0249. Adviser: Joan Morrissey. Thesis (M.Sc.)--University of Windsor (Canada), 2004

Quantum Limits of Interferometer Topologies for Gravitational Radiation Detection

In order to expand the astrophysical reach of gravitational wave detectors, several interferometer topologies have been proposed to evade the thermodynamic and quantum mechanical limits in future detectors. In this work, we make a systematic comparison among them by considering their sensitivities and complexities. We numerically optimize their sensitivities by introducing a cost function that tries to maximize the broadband improvement over the sensitivity of current detectors. We find that frequency-dependent squeezed-light injection with a hundred-meter scale filter cavity yields a good broadband sensitivity, with low complexity, and good robustness against optical loss. This study gives us a guideline for the near-term experimental research programs in enhancing the performance of future gravitational-wave detectors.Comment: grammar correcte