On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them

A full-rank under-determined linear system of equations Ax = b has in general infinitely many possible solutions. In recent years there is a growing interest in the sparsest solution of this equation—the one with the fewest non-zero entries, measured by ∥x∥₀. Such solutions find applications in signal and image processing, where the topic is typically referred to as “sparse representation”. Considering the columns of A as atoms of a dictionary, it is assumed that a given signal b is a linear composition of few such atoms. Recent work established that if the desired solution x is sparse enough, uniqueness of such a result is guaranteed. Also, pursuit algorithms, approximation solvers for the above problem, are guaranteed to succeed in finding this solution.Armed with these recent results, the problem can be reversed, and formed as an implied matrix factorization problem: Given a set of vectors {b_i}, known to emerge from such sparse constructions, Ax_i = b_i, with sufficiently sparse representations x_i, we seek the matrix A. In this paper we present both theoretical and algorithmic studies of this problem. We establish the uniqueness of the dictionary A, depending on the quantity and nature of the set {b_i}, and the sparsity of {x_i}. We also describe a recently developed algorithm, the K-SVD, that practically find the matrix A, in a manner similar to the K-Means algorithm. Finally, we demonstrate this algorithm on several stylized applications in image processing.     

混合激励线性预测语音编码标准中线谱频率量化的研究

线谱频率(Line Spectral Frequency,LSF)是线性预测频谱系数(Linear Predication Coefficient,LPC)有效的编码形式。语音线性预测模型中,LPC反映了声道调制的模型,是影响语音听觉感知重要的参数之一。在混合激励线性预测语音编码(Mixed Excitation Linear Prediction,MELP)标准中,对LSF采用4级码本进行分级式矢量量化。首先,为减少其量化冗余度以降低编码速率,本文提出了一种改进的选择算法,生成了一个2级码本替换之。其次,为提高合成语音质量,依据LSF矢量量化的精度与合成语音质量的关系的实验结果,提出根据人耳听觉感知特性进行LSF量化和评价的方法,并予以实验证明。     

A contemporary review on user scheduling techniques and feedback reduction strategies towards the development of 5G and beyond communications

User scheduling (US) is the process of dynamic selection of the set of active users out of all available users to serve in each time slot. This is done to optimize the system performance, such as maximizing the sum rate, achieving better fairness, and quality of service or minimizing the interference. The choice of US method depends on the desired system performance and the trade-off between fairness and efficiency. In order to achieve these performance metrics base station (BS) needs channel state information (CSI) of each user for efficient US. Moreover, US and CSI feedback are closely related in the context of conventional multiple-input multiple-output (MIMO) to massive MIMO (mMIMO) systems based on full and limited CSI, as feedback information is often used to make informed decisions on US. To address these objectives simultaneously, this survey deals with exploring different algorithms used for efficient US, various criteria for US considering different scenarios, key methods for user grouping, methods for reduced feedback, and different standard codebook based feedback methods. To be more specific and concise, this article provides a comprehensive survey on state of the art methods used for US in single cell single tier, dual stage (double tier), multi cell scenarios and feedback mechanisms used in various contexts, e.g., multiuser (MU)-MIMO, MU-mMIMO, frequency division duplexing (FDD) mMIMO framework. Moreover, a synopsis of the recently proposed advanced codebook and non-codebook based methods for the long term evolution standards, fifth generation, and beyond communications are discussed. Finally the research gaps as the future scopes are discussed in this article.