Image restoration problems are often solved by finding the minimizer of a suitable objective function. Usually this function consists of a data-fitting term and a regularization term. For the least squares solution, both the data-fitting and the regularization terms are in the 2 norm. In this paper, we consider the least absolute deviation (LAD) solution and the least mixed norm (LMN) solution. For the LAD solution, both the data-fitting and the regularization terms are in the 1 norm. For the LMN solution, the regularization term is in the 1 norm but the data-fitting term is in the 2 norm. Since images often have nonnegative intensity values, the proposed algorithms provide the option of taking into account the nonnegativity constraint. The LMN and LAD solutions are formulated as the solution to a linear or quadratic programming problem which is solved by interior point methods. At each iteration of the interior point method, a structured linear system must be solved. The preconditioned conjugate gradient method with factorized sparse inverse preconditioners is employed to solve such structured inner systems. Experimental results are used to demonstrate the effectiveness of our approach. We also show the quality of the restored images, using the minimization of mixed 2-1 and 1-1 norms, is better than that using only the 2 norm.
The problem of nonlinear dimensionality reduction is considered. We focus on problems where prior information is available, namely, semi-supervised dimensionality reduction. It is shown that basic nonlinear dimensionality reduction algorithms, such as Locally Linear Embedding (LLE), Isometric feature mapping (ISOMAP), and Local Tangent Space Alignment (LTSA), can be modified by taking into account prior information on exact mapping of certain data points. The sensitivity analysis of our algorithms shows that prior information will improve stability of the solution. We also give some insight on what kind of prior information best improves the solution. We demonstrate the usefulness of our algorithm by synthetic and real life examples.
Conserving the energy for motion is an important yet notwell-addressed problem in mobile sensor networks. In this paper, we study the problem of optimizing sensor movement for energy efficiency. We adopt a complete energy model to characterize the entire energy consumption in movement. Based on the model, we propose an optimal velocity schedule for minimizing energy consumption when the road condition is uniform; and a near optimal velocity schedule for the variable road condition by using continuous-state dynamic programming. Considering the variety in motion hardware, we also design one velocity schedule for simple microcontrollers, and one velocity schedule for relatively complex microcontrollers, respectively. Simulation results show that our velocity planning may have significant impact on energy conservation.
Conserving the energy for motion is an important yet not-well-addressed problem in mobile sensor networks. In this article, we study the problem of optimizing sensor movement for energy efficiency. We adopt a complete energy model to characterize the entire energy consumption in movement. Based on the model, we propose an optimal trapezoidal velocity schedule for minimizing energy consumption when the road condition is uniform; and a corresponding velocity schedule for the variable road condition by using continuous-state dynamic programming. Considering the variety in motion hardware, we also design one velocity schedule for simple microcontrollers, and one velocity schedule for relatively complex microcontrollers, respectively. Simulation results show that our velocity planning may have significant impact on energy conservation.
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