Abstract—This paper presents an unsupervised deep learning approach to online sparse signal extraction. For a batch of input vectors of low-rank and sparse components, a U-Net-based model is trained with a combination of nuclear and l1 norms as a loss function so as to encode and decodeonly the sparse component of each input vector. Since themodel learns general structures common to the sparsecomponents of the input vectors, it has the potential todistinguish them not only from low-rank but also from anybackground. After the training, the model can extract alearned sparse component from any input signal with muchlower computational complexity than iterative algorithms ofrobust principal component analysis (RPCA). In anapplication to respiratory auscultation, continuousadventitious sounds can be extracted as the sparsecomponents of the spectrograms of input auscultationsignals. It is experimentally demonstrated that a well-generalized model that outperforms RPCA can be obtainedby learning only a few hundreds of windowed signals of anauscultatory sound. 

Index Terms—nuclear loss, dual frame U-Net, low-rank and sparse model, lung sound analysis

Cite: Takumi Onomichi*, Tomoya Sakai, and Yasushi Obase, "Unsupervised Deep Learning of Sparse Signals against Low-Rank Backgrounds with Application to Online Lung Sound Separation," International Journal of Signal Processing Systems, Vol. 11, No. 1, pp. 1-6, March 2022. doi: 10.18178/ijsps.11.1.1-6