Inverse Problems

—Hough transform (HT) is a typical method to detect or segment geometry objects from images. In this paper, we study the principle of Hough Transform and its mathematical expressions, and try to use a new approach based on Hough transform for quick line and circle detection in image processing. Our method accurately detected some simple graphics, such as straight line of different direction, circles of different detection, thickness and different number. The results show that our method is less memory consumption and calculated fast, which could be applied for line detection and segmentation in 3D ultrasonic image.

In this paper, the deterministic parameter identification procedure proposed in a companion paper is applied to suction-dependent elasto-plasticity problems. A mathematical model for such type of problems is firstly presented, then it is applied to the parameter identification using laboratory data. The identification procedure is applied in a second example to exploitation of a gas reservoir. The effects of the

This paper concerns the reconstruction of an anisotropic conductivity tensor $\gamma$ from internal current densities of the form $J = \gamma\nabla u$, where $u$ solves a second-order elliptic equation $\nabla\cdot(\gamma\nabla u) = 0$ on a bounded domain $X$ with prescribed boundary conditions. A minimum number of such functionals equal to $n + 2$, where $n$ is the spatial dimension, is sufficient to guarantee a local reconstruction. We show that $\gamma$ can be uniquely reconstructed with a loss of one derivative compared to errors in the measurement of $J$. In the special case where $\gamma$ is scalar, it can be reconstructed with no loss of derivatives. We provide a precise statement of what components may be reconstructed with a loss of zero or one derivatives.

Bregman iterative algorithms have been extensively used for l1 and TV regularization problems,
allowing to obtain simple, fast and effective algorithms. In this paper, a coordinate descent algorithm for
geosounding inversion is modified by including a Bregman iterative procedure in the linearization.
Modeling results are presented for synthetic data, observing better convergence properties than the original
versions, avoiding the need of the continuation descent procedure.

In this paper, we derive a principal component regression (PCR) method for estimating the optical flow between frames of video sequences according to a pel-recursive manner. This is an easy alternative to dealing with mixtures of motion vectors due to the lack of too much prior information on their statistics (although they are supposed to be normal). The 2D motion vector estimation takes into consideration local image properties. The main advantage of the developed procedure is that no knowledge of the noise distribution is necessary. Preliminary experiments indicate that this approach provides robust estimates of the optical flow. KEY WORDS Motion estimation, principal component regression, and surveillance. 1.

Many works related learning from examples to regularization techniques for inverse problems, emphasizing the strong algorithmic and conceptual analogy of certain learning algorithms with regularization algorithms. In particular it is well known that regularization schemes such as Tikhonov regularization can be effectively used in the context of learning and are closely related to algorithms such as support vector machines. Nevertheless the connection with inverse problem was considered only for the discrete (finite sample) problem and the probabilistic aspects of learning from examples were not taken into account. In this paper we provide a natural extension of such analysis to the continuous (population) case and study the interplay between the discrete and continuous problems. From a theoretical point of view, this allows to draw a clear connection between the consistency approach in learning theory and the stability convergence property in ill-posed inverse problems. The main mat...

Rooms for music are often designed starting from a shape known from past experience to perform well acoustically. We reverse this design process by defining an acoustical signature and using it to generate novel room shapes. Our method builds off previous research on reconstructing room shapes from recorded impulse responses, but takes an instrumental rather than forensic approach, opening a range of unforeseen geometrical possibilities to the designer.

A custom-built sound signature design interface allows the user to adjust the location of image sources and listen to their impact on the convolution of an anechoic signal. Each image source is then used to derive a solution space for first and second-order reflections at a receiver position. As the user explores the solution space, planar surfaces are constructed at the reflection points, their perimeters expanded to make the image source audible to a larger receiver area. The user is free to select a particular surface geometry from the solution space based on aesthetic, functional or other criteria knowing that the acoustic contribution of the surfaces will remain consistent.

Along with presenting how we have applied acoustic reverse-engineering to a range of design projects, we outline a proof of concept study in which we compared objective parameters for a number of different room shapes derived from the same acoustical signature.

Literature on Unified Modeling Language (UML) and aspect-orientation often focus on improving the software development process [2]. This paper presents a systems engineering perspective that motivates an aspect-oriented software architectural analysis approach using ...

NP Complete (abbreviated as NPC) problems, standing at the crux of deciding whether P=NP, are among hardest problems in computer science and other related areas. Through decades, NPC problems are
treated as one class. Observing that NPC problems have different natures, it is unlikely that they will have the same complexity. Our intensive study shows that NPC problems are not all equivalent in computational complexity, and they can be further classified. We then show that the classification of NPC problems may depend on their natures, reduction methods, exact algorithms, and the boundary between P and NP. And a new perspective is provided: both P problems and NPC problems have the duality feature in terms of
computational complexity of asymptotic efficiency of algorithms. We also discuss about the NPC problems in real-life and shine some lights on finding better solutions to NPC problems.

In this paper the problem of recovering a regularized solution of the Fredholm integral equations of the first kind with Hermitian and square-integrable kernels, and with data corrupted by additive noise, is considered. Instead of using a variational regularization of Tikhonov type, based on a priori global bounds, we propose a method of truncation of eigenfunction expansions that can be proved to converge asymptotically, in the sense of the L^2--norm, in the limit of noise vanishing. Here we extend the probabilistic counterpart of this procedure by constructing a probabilistically regularized solution without assuming any structure of order on the sequence of the Fourier coefficients of the data. This probabilistic approach allows us to use the statistical tools proper of time-series analysis, and in this way we attain a new regularizing algorithm, which is illustrated by some numerical examples. Finally, a comparison with solutions obtained by the means of the variational regulari...

Some iterative matrix relations for the geometric, kinematic and dynamic analysis of a Delta parallel robot are established in this paper. The prototype of this manipulator is a three degree of freedom spatial mechanism, which consists of a system of parallel chains. Supposing that the position and the translation motion of the platform are known, an inverse dynamic problem is solved using the virtual powers method. Finally, some recursive matrix relations and some graphs for the moments and the powers of the three active couples are determined.

The investigation of the earth's internal structure is of great interest in
areas as diverse as civil engineering, water management and oil
exploration. A common technique looks to estimate the electrical
conductivity of the subsurface, a proxy for the internal structure, from a
grid of surface voltage measurements - an example of an ill-posed
inverse problem. This paper uses a Bayesian modeling approach to
compare different prior model descriptions using Markov chain Monte
Carlo estimation. A range of simulation examples are considered.

Karst aquifers are characterized by extreme heterogeneity due to the presence of karst conduits embedded in a fractured matrix having a much lower hydraulic conductivity. The resulting contrast in the physical properties of the system implies that the system reacts very rapidly to some changes in the boundary conditions and that numerical models are extremely sensitive to small modifications in properties or positions of the conduits. Furthermore, one major issue in all those models is that the location and size of the conduits is generally unknown. For all those reasons, estimating karst network geometry and their properties by solving an inverse problem is a particularly difficult problem. In this paper, two numerical experiments are described. In the first one, 18,0 0 0 flow and transport simulations have been computed and used in a systematic manner to assess statistically if one can retrieve the parameters of a model (geometry and radius of the conduits, hydraulic conductivity of the conduits) from head and tracer data. When two tracer test data sets are available, the solution of the inverse problems indicate with high certainty that there are indeed two conduits and not more. The radius of the conduits are usually well identified but not the properties of the matrix. If more conduits are present in the system, but only two tracer test data sets are available, the inverse problem is still able to identify the true solution as the most probable but it also indicates that the data are insufficient to conclude with high certainty. In the second experiment, a more complex model (including non linear flow equations in conduits) is considered. In this example, gradient-based optimization techniques are proved to be efficient for estimating the radius of the conduits and the hydraulic conductivity of the matrix in a promising and efficient manner. These results suggest that, despite the numerical difficulties, inverse methods should be used to constrain numerical models of karstic systems using flow and transport data. They also suggest that a pragmatic approach for these complex systems could be to generate a large set of karst conduit network realizations using a pseudo-genetic approach such as SKS, and for each karst realization, flow and transport parameters could be optimized using a gradient-based search such as the one implemented in PEST.

The paper presents a cognitive architecture for solution of inverse kinematics problem (IKP) of 6-DOF elbow manipulator with spherical wrist by Locally Recurrent Neural Networks (LRNNs) and simulated the solution by using MATLAB/Simulink. This design is aimed to allow the manipulator system to perform complex movement operations by solving the Inverse Kinematic Problem (IKP) with LRNNs by using the position and orientation of end-effector which represent by wrist with 3-DOF. The Levenberg-Marquardt back propagation (LMBP) is used in the learning of LRNNs which offered the high computation and accuracy for solving IKP for manipulator. This model permits direct forward dynamics simulation, which accurately predicts wrist position, also present a solution to the inverse problem of determining set of joints angle to achieve a given command for posture of manipulator. The simulation of design achieved by connect the program with SimulinkMATLAB Ver. 2009b to calculate the forward and inverse kinematic and implement the movements manipulator. Satisfactory results are obtained, that explains the ability of implement the posture of 6-DOF manipulator by calculate the kinematic with LRNNs and implement high complex movements.

Stress inversions are a useful and popular tool for structural geologist and seismologist alike. These methods were first introduced by Wallace (1951) and Bott (1959) and subsequent studies continue to be based on their assumptions: the remote stress tensor is spatially uniform for the rock mass containing the faults and temporally constant over the history of faulting in that region, and the slip on each fault surface has the same direction and sense as the maximum shear stress resolved on that surface from the remote stress tensor. Furthermore, successful implementation requires that slip accumulates on faults of diverse orientation. Many studies employ these methods on isolated faults or on fault systems with limited ranges of orientations, which can lead to erroneous results. We propose a new method that incorporates the effects of mechanical interaction of the entire fault or fault system, and solves the complete mechanical problem rather than employing empirical relationships between slip and stress or strain (or strain rate). The method requires knowledge of the fault geometry and information on at least one slip vector component along portions of the known fault geometry. For example, if throw is known, the strike-slip component can be solved for. We test the method using a single synthetic fault with anisotropic roughness similar to that measured at fault outcrops. While the orientation of remote stress may be determined precisely, the lack of diverse fault orientations introduces a systematic error in the remote stress ratio. We further test the effect of diversity of fault orientations and find that Wallace–Bott type inversions do not perform as well for limited ranges of orientations when compared to the proposed method. Finally, we use published data from the 1999 Chi-Chi, Taiwan, earthquake, and find that the method using surface data only, and surface data with subsurface focal mechanisms, produce similar results. The resulting stress orientations are in good agreement with results from Wallace–Bott inversions. Furthermore, the slip distribution is in general agreement with kinematic slip inversions using coseismic surface deformation. Stress inversion methods using fault slip data can thus be improved upon, significantly in some cases, by solving a mechanical boundary value problem that takes into account the geometry of faults or fault systems. As a bonus, the solution provides the stress, strain, and displacement fields throughout the region and the slip distributions on the faults.► New method for stress inversion incorporates the effects of interaction of faults. ► Errors in tests cases are smaller than those of faultless (Wallace-Bott) inversions. ► Using slip data from Chelungpu fault reproduces slip distribution well. ► New method provides a useful alternative to faultless inversion methods.

Data assimilation systems allow for estimating surface fluxes of
greenhouse gases from atmospheric concentration
measurements. Good knowledge about fluxes is essential to
understand how climate change affects ecosystems and to
characterize feedback mechanisms.  Based on assimilation of more
than one year of atmospheric in-situ concentration measurements,
we compare the performance of two established data assimilation
models, CarbonTracker and TM5‑4DVar, for CO₂ flux
estimation. CarbonTracker uses an Ensemble Kalman Filter method
to optimize fluxes on ecoregions. TM5‑4DVar employs a 4-D
variational method and optimizes fluxes on a 6°×4°
longitude/latitude grid. Harmonizing the input data allows
analyzing the strengths and weaknesses of the two approaches by
direct comparison of the modelled concentrations and the
estimated fluxes.  We further assess the sensitivity of the two
approaches to the density of observations and operational
parameters such as the length of the assimilation time window.

Our results show that both models provide optimized CO₂
concentration fields of similar quality. In Antarctica
CarbonTracker underestimates the wintertime CO₂ concentrations,
since its 5-week assimilation window does not allow for adjusting
the far-away surface fluxes in response to the detected
concentration mismatch. Flux estimates by CarbonTracker and
TM5‑4DVar are consistent and robust for regions with good
observation coverage, regions with low observation coverage
reveal significant differences. In South America, the fluxes
estimated by TM5‑4DVar suffer from limited representativeness of
the few observations. For the North American continent, mimicking
the historical increase of measurement network density shows
improving agreement between CarbonTracker and TM5‑4DVar flux
estimates for increasing observation density.