结构化稀疏分解与压缩感知实现音频信号有损压缩

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"本文提出了一种利用结构化稀疏分解和压缩感知技术进行有损音频信号压缩的方法。通过使用LASSO（最小绝对收缩选择算子）将音频信号分解为音调层和瞬态层，并对这两层分别采用压缩感知方法进行压缩。引入新的惩罚项，利用变换系数的结构信息，LASSO可以实现比传统方法更好的音频信号稀疏逼近。此外，还提出了一个稀疏性分配算法，动态调整两个结果层之间的稀疏度，从而提升压缩感知的性能。实验结果显示，新方法的压缩性能优于传统方法。" 在本文中，作者探讨了一个创新的音频压缩技术，它结合了结构化稀疏分解和压缩感知的概念。这项技术的目标是实现有损音频信号的高效压缩，以减小存储空间和传输带宽的需求。首先，他们采用LASSO进行信号分解。LASSO是一种线性模型选择和变量选择的方法，它通过最小化残差平方和的同时，对系数施加一个L1范数惩罚，促使模型系数向量具有稀疏性。在音频信号处理中，LASSO被用来将音频信号分解为两个主要成分：音调层（代表持续且稳定的音调部分）和瞬态层（代表短暂的、非平稳的声音事件）。这种分解有助于区分音频的不同特性，以便于后续处理。接下来，引入压缩感知理论。压缩感知是一种理论，允许以远低于奈奎斯特定理所要求的速率对信号进行采样，仍能重构信号。在这个过程中，两个分解出的层都通过压缩感知算法进行压缩，以减少数据量，同时保持可接受的信号质量。为了进一步优化压缩效果，作者设计了一个新的惩罚项，该惩罚项考虑了变换系数的结构信息。这使得LASSO能够更准确地捕捉音频信号的内在结构，从而得到更好的稀疏近似。此外，他们还提出了一种稀疏性分配算法。这个算法动态调整音调层和瞬态层之间的稀疏程度，以适应不同类型的音频内容。通过对不同层的稀疏度进行优化，可以提高压缩感知的效率和压缩后的信号质量。实验结果证实了这种方法的有效性，显示新方法在保持音质的同时，提供了优于传统音频压缩技术的压缩性能。这表明，结合结构化稀疏分解和压缩感知的新方法对于音频信号压缩领域是一个重要的进步，有可能被广泛应用于音频编码、存储和传输等领域。

LOSSY AUDIO SIGNAL COMPRESSION VIA STRUCTURED SPARSE DECOMPOSITION

AND COMPRESSED SENSING

Sumxin Jiang, Rendong Ying, Zhenqi Lu, Peilin Liu and Zenghui Zhang

Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, China

liupeilin@sjtu.edu.cn

ABSTRACT

In this paper, we propose a method for lossy audio signal

compression via structured sparse decomposition and com-

pressed sensing (CS). In this method, a least absolute shrink-

age and selection operator (LASSO) is employed to sparse

and structured decompose the audio signals into tonal and

transient layers, and then, both resulting layers are com-

pressed by a CS method. By employing a new penalty term,

which takes advantage of the structure information of trans-

form coefﬁcients, the LASSO is able to achieve a better sparse

approximation of the audio signal than traditional methods

do. In addition, we propose a sparsity allocation algorithm,

which adjusts the sparsity between the two resulting layers,

thus improving the performance of CS. Experimental results

showed that the new method provided a better compression

performance than conventional methods did.

Index Terms— Compressed sensing, sparse approxima-

tion, audio compression, Lasso

1. INTRODUCTION

The ascending theory of compressed sensing (CS) [1], [2] is

a sub-Nyquist sampling strategy, which combines data acqui-

sition with data compression to enable a new generation of

signal acquisition scheme. This novel acquisition scheme op-

erates near the intrinsic information rate of the signal rather

than its ambient data rate [3], thus substantially surpassing

the limitations of classical Nyquist sampling theory. The CS

theory is constructed on the assumption that the signal has a

sparse or compressible linear representation in a predeﬁned

dictionary. Therefore, the construction of an appropriate dic-

tionary is one of the key issues in CS theory.

With respect to the CS for audio signals [4], [5], ﬁnding

a dictionary, on which the audio signals can be well sparsely

represented, is usually the primary task. As the audio sig-

nals are time-varying and consequently can hardly be well

sparsely decomposed within a single orthogonal dictionary

[6], sub-optimal methods [7], [8], which achieve the best s-

parse approximation of the audio signal, are proposed in re-

This work was partially supported by the National Natural Science Foun-

dation of China under grant number 61171171 and 61102169.

cent years. Most of these methods are based on the struc-

ture properties of the audio signal in a certain transform do-

main. M. Kowalski and B. Torresani [9] found that the s-

parse and structured audio signal decomposition on dictionar-

ies can be achieved through explicit modeling in coefﬁcient

domain. They reformulated the sparse decomposition of au-

dio signals as a regression problem, which can be resolved

using a least absolute shrinkage and selection operator (LAS-

SO) with mixed-norm constraints [10], [11]. In their work, a

family of structured shrinkage operators are implemented and

evaluated, such as Elitist LASSO (E-LASSO), Group LASSO

(G-LASSO), and Elitist-Group LASSO (EG-LASSO). How-

ever, these operators can hardly utilize the dependencies a-

mong the neighborhoods within different coefﬁcient groups

(inter-dependencies). To exploit the inter-dependencies and

to introduce more ﬂexibility in the coefﬁcient domain model-

ing, the authors [12] further proposed the social sparsity con-

vex operators. With these social sparsity convex operators,

the audio signals, which exhibit obvious structures in the co-

efﬁcient domain, can be efﬁciently and sparsely decomposed,

if a suitable set of weighted neighborhoods is selected.

In this paper, a new audio compression method, which

combines the social convex operators with CS theory, is pro-

posed. Audio signals are usually composed of tonal compo-

nents, which are sparse in time domain, and transient com-

ponents, which are sparse in frequency domain [13]. Consid-

ering these structure properties, we ﬁrst use the social con-

vex operators to decompose the audio signals into tonal and

transient layers, and then, further compress the two resulting

layers using a CS method. As the convex operators can make

full use of the structure information in coefﬁcient domain, the

obtained tonal and transient components will form a ﬁne ap-

proximation to the original audio signal. Moreover, a new

weighted neighborhood window is proposed for the convex

operator, thus improving the performance of sparse decom-

position. In addition, because of the time-varying property of

audio signals, which leads to a non-constant ratio of the tonal

and transient layers, an algorithm is presented to allocate the

sparsity between the two layers, thus substantially improving

the performance of the CS method.

The organization of this paper is as follows. Section 2

introduces the structured shrinkage operators used for audio

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