Joint and Direct Optimization for Dictionary Learning in Convolutional Sparse Representation.

Convolutional sparse coding (CSC) is a useful tool in many image and audio applications. Maximizing the performance of CSC requires that the dictionary used to store the features of signals can be learned from real data. The so-called convolutional dictionary learning (CDL) problem is formulated within a nonconvex, nonsmooth optimization framework. Most existing CDL solvers alternately update the coefficients and dictionary in an iterative manner. However, these approaches are prone to running redundant iterations, and their convergence properties are difficult to analyze. Moreover, most of those methods approximate the original nonconvex sparse inducing function using a convex regularizer to promote computational efficiency. This approach to approximation may result in nonsparse representations and, thereby, hinder the performance of the applications. In this paper, we deal with the nonconvex, nonsmooth constraints of the original CDL directly using the modified forward-backward splitting approach, in which the coefficients and dictionary are simultaneously updated in each iteration. We also propose a novel parameter adaption scheme to increase the speed of the algorithm used to obtain a usable dictionary and in so doing prove convergence. We also show that the proposed approach is applicable to parallel processing to reduce the computing time required by the algorithm to achieve convergence. The experimental results demonstrate that our method requires less time than the existing methods to achieve the convergence point while using a smaller final functional value. We also applied the dictionaries learned using the proposed and existing methods to an application involving signal separation. The dictionary learned using the proposed approach provides performance superior to that of comparable methods.

Adaptive ADMM for Dictionary Learning in Convolutional Sparse Representation.

In this paper, we propose a novel approach to convolutional sparse representation with the aim of resolving the dictionary learning problem. The proposed method, referred to as the adaptive alternating direction method of multipliers (AADMM), employs constraints comprising non-convex, non-smooth terms, such as the l0 -norm imposed on the coefficients and the unit-norm sphere imposed on the length of each dictionary element. The proposed scheme incorporates a novel parameter adaption scheme that enables ADMM to achieve convergence more quickly, as evidenced by numerical and theoretical analysis. In experiments involving image signal applications, the dictionaries learned using AADMM outperformed those learned using comparable dictionary learning methods.

Interlayer bit allocation for scalable video coding.

In this paper, we present a theoretical analysis of the distortion in multilayer coding structures. Specifically, we analyze the prediction structure used to achieve temporal, spatial, and quality scalability of scalable video coding (SVC) and show that the average peak signal-to-noise ratio (PSNR) of SVC is a weighted combination of the bit rates assigned to all the streams. Our analysis utilizes the end user's preference for certain resolutions. We also propose a rate-distortion (R-D) optimization algorithm and compare its performance with that of a state-of-the-art scalable bit allocation algorithm. The reported experiment results demonstrate that the R-D algorithm significantly outperforms the compared approach in terms of the average PSNR.

Subband weighting with pixel connectivity for 3-D wavelet coding.

Performing optimal bit-allocation with 3-D wavelet coding methods is difficult because energy is not conserved after applying the motion-compensated temporal filtering (MCTF) process and the spatial wavelet transform. The problem cannot be solved by extending the 2-D wavelet coefficients weighting method directly and then applying the result to 3-D wavelet coefficients, since this approach does not consider the complicated pixel connectivity that results from the lifting-based MCTF process. In this paper, we propose a novel weighting method, which takes account of the pixel connectivity, to solve the problem and derive the effect of the quantization error of a subband on the reconstruction error of a group of pictures. We employ the proposed method on a 2-D + t structure with different temporal filters, namely the 5-3 filter and the 9-7 filter. Experiments on various coding parameters and sequences show that the proposed approach improves the bit-allocation performance over that obtained by using the weightings derived without considering the pixel connectivity in the MCTF process.