Multilevel Decomposition Algorithm Research Articles

Hybrid Multi-level Regularizations with Sparse Representation for Single Depth Map Super-Resolution

Limited spatial resolution and varieties of degradations are the main restrictions of today’s captured depth map by active 3D sensing devices. Typical restrictions limit the direct use of the obtained depth maps in most of 3D applications. In this paper, we present a single depth map upsampling approach in contrast to the common work of using the corresponding combined color image to guide the upsampling process. The proposed approach employs a multi-level decomposition to convert the depth upsampling process to a classification-based problem via a multi-level classification-based learning algorithm. Hence, the lost high frequency details can be better preserved at different levels. The adopted multi-level decomposition algorithm utilizes $$l_{1} ,$$ and $$l_{0}$$ sparse regularization with total-variation regularization to keep structure- and edge-preserving smoothing with robustness to noisy degradations. In addition, the proposed classification-based learning algorithm supports the accuracy of discrimination by learning discriminative dictionaries that carry original features about each class and learning common shared dictionaries that represent the shared features between classes. The proposed algorithm has been validated via different experiments under variety of degradations using different datasets from different sensing devices. Results show superiority to the state of the art, especially in case of upsampling noisy low-resolution depth maps.

Multilevel decomposition of vibration signals from motorcycles using the wavelet–Hilbert transformation

To maximize comfort and safety it is important to control motorcycle vibration. In order to assess the vibration of motorcycles, measurements need to be taken from these machines. Vibration signals acquired using sensors mounted on the machine always include the excitation components from the engine, the road surface, and the structure of the motorcycle frame. Generally, these vibration signals are coupled together. Presently, there is no ideal method to separate these signal components to allow better analysis of the different contributing factors. Contributions to the total vibration signal from the main vibration sources (the engine and the road surface) cannot be determined exactly. To solve this problem, a multilevel decomposition algorithm based on the wavelet–Hilbert transform is proposed in this paper. The paper formulates the vibration signal model for a motorcycle and discusses the performance of the multilevel decomposition algorithm using simulation and experimental methods. The simulation and experimental results show that the proposed new algorithm is an effective method for the identification of vibration sources on a motorcycle.

Convex multilevel decomposition algorithms for non‐monotone problems

AbstractA convex, multilevel decomposition algorithm is proposed in this paper for the solution of static analysis problems involving non‐monotone, possibly multivalued laws. The theory is developed here for a model structure with non‐monotone interface or boundary conditions. First the non‐monotone laws are written in the form of a difference of two monotone functions. Under this decomposition, the non‐linear elastostatic analysis problem is equivalent to a system of convex variational inequalities and to non‐convex min‐min problems for appropriately defined Lagrangian functions. The solution(s) of each one of the aforementioned problems describe the position(s) of static equilibrium of the considered structure. In this paper a multilevel optimization scheme, due to Auchmuty,1 is used for the numerical solution of the problem. The most interesting feature of this method, from the computational mechanics' standpoint, is the fact that each one of the subproblems involved in the multilevel algorithm is a convex optimization problem, or, in terms of mechanics, an appropriately modified monotone ‘unilateral’ problem. Thus, existing algorithms and software can be used for the numerical solution with minor modifications. Numerical results concerning the calculation of elastic and rigid stamp problems and of material inclusion problems with delamination and non‐monotone stick‐slip frictional effects illustrate the theory.