Abstract. Multilayer convolutional sparse coding (ML-CSC) is a powerful technique for obtaining parsimonious representations of signals in machine learning applications. However, achieving maximum parsimony without sacrificing data fidelity requires learning a dictionary from data, resulting in the nonconvex nonsmooth optimization problem of multilayer convolutional dictionary learning (ML-CDL). Existing ML-CDL solvers derived from traditional dictionary learning employ the convex [Formula: see text] function as the sparsity-inducing function to promote convergence; nevertheless, analyzing the convergence of candidate alternate optimization schemes is still challenging. In this paper, we reformulate the ML-CDL problem by replacing the convolution with the Hadamard product to reduce computational complexity, and to achieve this without destroying the consistency between the variables in the time and frequency domains, additional constraints are introduced to the reformulated problem. We also modify a forward-backward splitting algorithm to solve the reformulated ML-CDL problem using simultaneous coefficients and dictionary element updates across all layers. In contrast, these variables are updated alternately in the previous approaches. The proposed algorithm includes a parameter adaptation scheme to improve optimization performance and ensure convergence. In numerical simulations, the proposed method outperforms existing methods by achieving convergence in fewer iterations and generating a smaller final functional value. The high quality of recovered images demonstrates the applicability of multilayer sparse representation to image reconstruction.

In light of the rapid advancements in quantum computing, the synthesis of quantum circuits has drawn significant attention. Quantum circuits are required to be reversible owing to their inherent physical characteristics. However, synthesizing such circuits and optimizing their performance present substantial challenges. In this paper, we proposed to adopt reinforcement learning for synthesizing the reversible circuits involving NOT, CNOT, Toffoli, and other relevant gates and, in doing so, minimize the quantum computational costs of the resulting circuits. The experimental results demonstrated that the reversible circuits generated using the proposed method outperform the prior methods in both the gate counts and the total cost.

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.

In this paper, we formulated the optimal bit-allocation problem for a scalable codec for images/videos as a graph-based constrained vector-valued optimization problem with many optimal solutions, which are referred to as Pareto points. Pareto points are generally derived using weighted sum scalarization; however, it has yet to be determined whether all Pareto points can be derived using this approach. This paper addresses this issue. When presented as a theorem, our results indicate that as long as the rate-distortion function of each resolution is strictly decreasing and convex and the Pareto points form a continuous curve, then all Pareto points can be derived using scalarization. The theorem is verified using the state-of-the-art scalable coding method H.264/SVC and a scalability extension of High Efficiency Video Coding (HEVC). We highlight a number of easily interpretable Pareto points that represent a good trade-off between candidate resolutions. The proximity point is defined as the Pareto point closest to the ideal performance for each resolution. We also model the Pareto points as a function of total bit rate and demonstrate that the Pareto points at other target bit rates can be predicted.

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, nonsmooth 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.

Signal separation has a fundamental role in many image applications, such as noise removing (white noise, reflection, rain, etc), segmentation, and inpainting. To fulfill signal separation, morphological component analysis (MCA) has been widely deployed in a plenty of applications [1], [2], [3]. MCA uses dictionaries to model morphologies of subcomponents, but the coherence between dictionaries may cause the defect presenting in the obtained subcomponents [4], [5]. In this article, we replace the sparse coding of MCA with the weighted sparse coding, and by assigning heavier weights to dictionaries' highly coherent atoms, the defect presenting in the obtained subcomponents is reduced. The experimental results show that the proposed signal separation algorithm achieves a significant performance gain over MCA.

Morphological component analysis (MCA) for signal separation decomposes a signal into a super-position of morphological subcomponents, each of which is approximately sparse in a certain dictionary. Some of the dictionaries can also be modified to make them adaptive to local structure in images. We show that signal separation performance can be improved over the previous MCA approaches by replacing L1-norm optimization with “weighted” L1-norm optimization and replacing their dictionary adaptation with regularized dictionary adaptation. The weight on an atom for sparse coding is commonly derived from the corresponding coefficient's value. In contrast, the weight of an atom in a dictionary for signal separation is derived from the mutual coherence between the atom and the atoms in the other dictionaries. The proposed solution for regularized dictionary adaptation is an extension of the K-SVD method, where the dictionary and “weighted” sparse coefficients are estimated simultaneously. We present a series of experiments demonstrating the significant performance improvement of the proposed algorithm over the previous approaches for signal separation.

We investigate the wavelet-based scalable video coding problem and present a solution that takes account of each user's preferred resolution. Based on the preference, we formulate the bit allocation problem of wavelet-based scalable video coding. We propose three methods to solve the problem. The first is an efficient Lagrangian-based method that solves the upper bound of the problem optimally, and the second is a less efficient dynamic programming method that solves the problem optimally. Both methods require knowledge of the user's preference. For the case where the user's preference is unknown, we solve the problem by a min-max approach. Our objective is to find the bit allocation solution that maximizes the worst possible performance. We show that the worst performance occurs when all users subscribe to the same spatial, temporal, and quality resolutions. Thus, the min-max solution is exactly the same as the traditional bit allocation method for a non-scalable wavelet codec. We conduct several experiments on the 2D+t MCTF-EZBC wavelet codec with respect to various subscribers' preferences. The results demonstrate that knowing the users' preferences improves the coding performance of the scalable video codec significantly.

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.

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.

In this paper, we propose a novel way to derive the weighting for subbands that conserves energy. Once the weight of each subband has been calculated by motion-compensation temporal filtering, the effect of the quantization error of a subband on the reconstruction error of a group of pictures can be determined. Then, we weigh each subband and use the weighted coefficients to derive the optimal bit-allocation solution for 3-D wavelet coding methods. We apply the proposed method to bit-allocation on a 2D+t structure with a 5-3 temporal wavelet filter, and show that it achieves a 0.5–1.5 dB peak-signal-to-noise improvement over using the weighting of subbands on various coding parameters and sequences.