Research Of Audio Sparse Representation In Compressive Sensing

As the demanding of the quality of audio, image, video and othermedia increasing, the traditional coding mode, which sample signals atfirst and then do compression to the samples, gradually reveals itsdrawbacks: on one hand, in order to obtain high-quality media, traditionalencoding mode requires the use of a higher sampling rate to collect moresamples, while the sampler cannot afford such a high sampling rate; on theother hand, the requirements of transmission and storage claim thatcompression has to be done to the sampled data, discarding most of theredundant data, resulting in a waste of resources. This traditional codingmode greatly limits the development of multimedia technology. In recentyears, compressive sensing theory has a rapid rise. Compressive sensing is“do compressing while sampling”. Compared to the traditional codingmode, compressive sensing theory can highly probably reconstruct theoriginal signal with less observed values, even less values than the originalsignal. Thus, compressive sensing can break the constraint of the Nyquisttheorem and make it possible that signals can be sampled with sub-Nyquistfrequency.Although theoretically compressive sensing can achieve a highercompression ratio and reconstruction accuracy, and it has been researchedin the image and video applications. However, in fact, the performance isnot satisfactory and little has been done to the research and application ofcompressive sensing in audio. To solve the mentioned problems, this articlefocuses on research of sparse representation and construction of an audiocompressive sensing system. This article presents a new learning dictionary algorithm called K-means clustering empirical mode decomposition(K-EMD) dictionary learning method. The method makes decomposition totraining audio signals using empirical mode decomposition method. Thealgorithm extracts the intrinsic mode functions (IMF) and the trend parts.The algorithm applies the K-means clustering method to the extractedcompositions thus getting the learned dictionary. Meanwhile, in order toimprove the performance of sparse representation and accelerate theprocess of making compressive sensing technology from theory to practicalapplication, this paper presents a new audio compressive sensing codingmode. The goal of the new coding mode is to break the traditional mode ofunified audio coding mode which uses two separate sets of coding modes,thus this paper presents a coding mode which divides signals intosteady-state component, transient component and the residual componentusing Least Absolute Shrinkage and Selection Operator (LASSO), and thenprocess the three components separately. To audio signals, the steady-statecomponent is the tonal part of the signal, the transient component isimpulse part and the residual component includes noise and some weakinformation of the audio. For steady-state component, the spectralcompressive sensing technology is applied to it because of its harmoniccharacteristics; for transient component, the K-EMD based compressivesensing method is applied because of its time-domain waveforms aresimilar; for the residual component, the GAD (Greedy Adaptive Dictionary)based compressive sensing method is applied because the residual part hassome information of the original signal.In order to verify the performance of K-EMD learning dictionaryconstruction method proposed in this paper and verify the performance ofthe proposed system for audio, a lot of experiments have been done toverify the sparsity of the expansion coefficients using K-EMD dictionary,the reconstruction accuracy using K-EMD dictionary, the sparsity andreconstruction accuracy of the audio compressive sensing system. Theexperiments proved that the sparsity of expansion coefficients and reconstruction accuracy using K-EMD is57.46%and57.00%respectivelyhigher than that using K-SVD. The proposed audio system improvedsparsity of expansion coefficients and reconstruction accuracy with62.85%and56.30%respectively compared compressive sensing systemusing single sparse representation method.