Concatenated image completion via tensor augmentation and completion

This paper proposes a novel framework called concatenated image completion via tensor augmentation and completion (ICTAC), which recovers missing entries of color images with high accuracy. Typical images are second- or third-order tensors (2D/3D) depending if they are grayscale or color, hence tensor completion algorithms are ideal for their recovery. The proposed framework performs image completion by concatenating copies of a single image that has missing entries into a third-order tensor, applying a dimensionality augmentation technique to the tensor, utilizing a tensor completion algorithm for recovering its missing entries, and finally extracting the recovered image from the tensor. The solution relies on two key components that have been recently proposed to take advantage of the tensor train (TT) rank: A tensor augmentation tool called ket augmentation (KA) that represents a low-order tensor by a higher-order tensor, and the algorithm tensor completion by parallel matrix factorization via tensor train (TMac-TT), which has been demonstrated to outperform state-of-the-art tensor completion algorithms. Simulation results for color image recovery show the clear advantage of our framework against current state-of-the-art tensor completion algorithms.Comment: 7 pages, 6 figures, submitted to ICSPCS 201

Efficient tensor completion for color image and video recovery: Low-rank tensor train

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor train (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via tensor train (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher-orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.Comment: Submitted to the IEEE Transactions on Image Processing. arXiv admin note: substantial text overlap with arXiv:1601.0108

Time-resolved photoelectron spectroscopy of proton transfer in the ground state of chloromalonaldehyde: Wave-packet dynamics on effective potential surfaces of reduced dimensionality

We report on a simple but widely useful method for obtaining time-independent potential surfaces of reduced dimensionality wherein the coupling between reaction and substrate modes is embedded by averaging over an ensemble of classical trajectories. While these classically averaged potentials with their reduced dimensionality should be useful whenever a separation between reaction and substrate modes is meaningful, their use brings about significant simplification in studies of time-resolved photoelectron spectra in polyatomic systems where full-dimensional studies of skeletal and photoelectron dynamics can be prohibitive. Here we report on the use of these effective potentials in the studies of dump-probe photoelectron spectra of intramolecular proton transfer in chloromalonaldehyde. In these applications the effective potentials should provide a more realistic description of proton-substrate couplings than the sudden or adiabatic approximations commonly employed in studies of proton transfer. The resulting time-dependent photoelectron signals, obtained here assuming a constant value of the photoelectron matrix element for ionization of the wave packet, are seen to track the proton transfer