Nonnegative Matrix Factorization (NMF) is a promising data-driven matrix decomposition method, and is becoming very active and attractive in machine learning and blind source separation areas. So far NMF algorithm has been widely used in diverse applications, including image processing, anti-collision for Radio Frequency Identification (RFID) systems and audio signal analysis, and so on. However the typical NMF algorithms cannot work well in underdetermined mixture, i.e., the number of observed signals is less than that of source signals. In practical applications, adding suitable constraints fused into NMF algorithm can achieve remarkable decomposition results. As a motivation, this paper proposes to add the minimum volume and minimum correlation constrains (MCV) to the NMF algorithm, which makes the new algorithm named MCV-NMF algorithm suitable for underdetermined scenarios where the source signals satisfy mutual independent assumption. Experimental simulation results validate that the MCV-NMF algorithm has a better performance improvement in solving RFID tag anti-collision problem than that of using the nearest typical NMF method.

MUltiple SIgnal Classification (MUSIC) is a standard technique for direction of arrival (DOA) estimation with high resolution. However, MUSIC cannot estimate DOAs accurately in the case of underdetermined conditions, where the number of sources exceeds the number of microphones. To overcome this drawback, an extension of MUSIC using cumulants called 2q-MUSIC has been proposed, but this method greatly suffers from the variance of the statistics, given as the temporal mean of the observation process, and requires long observation. In this paper, we propose a new approach for extending MUSIC that exploits higher-order moments of the signal for the underdetermined DOA estimation with smaller variance. We propose an estimation algorithm that nonlinearly maps the observed signal onto a space with expanded dimensionality and conducts MUSIC-based correlation analysis in the expanded space. Since the dimensionality of the noise subspace is increased by the mapping, the proposed method enables the estimation of DOAs in the case of underdetermined conditions. Furthermore, we describe the class of mapping that allows us to analyze the higher-order moments of the observed signal in the original space. We compare 2q-MUSIC and the proposed method through an experiment assuming that the true number of sources is known as prior information to evaluate in terms of the bias-variance tradeoff of the statistics and computational complexity. The results clarify that the proposed method has advantages for both computational complexity and estimation accuracy in short-time analysis, i.e., the time duration of the analyzed data is short.

This paper deals with the problem of underdetermined blind source separation (BSS) where the number of sources is unknown. We propose a BSS approach that simultaneously estimates the number of sources, separates the sources based on the sparseness of speech, estimates the direction of arrival of each source, and performs permutation alignment. We confirmed experimentally that reasonably good separation was obtained with the present method without specifying the number of sources.

This survey provides a brief introduction to compressed sensing as well as several major algorithms to solve it and its various applications to communications systems. We firstly review linear simultaneous equations as ill-posed inverse problems, since the idea of compressed sensing could be best understood in the context of the linear equations. Then, we consider the problem of compressed sensing as an underdetermined linear system with a prior information that the true solution is sparse, and explain the sparse signal recovery based on 1 optimization, which plays the central role in compressed sensing, with some intuitive explanations on the optimization problem. Moreover, we introduce some important properties of the sensing matrix in order to establish the guarantee of the exact recovery of sparse signals from the underdetermined system. After summarizing several major algorithms to obtain a sparse solution focusing on the 1 optimization and the greedy approaches, we introduce applications of compressed sensing to communications systems, such as wireless channel estimation, wireless sensor network, network tomography, cognitive radio, array signal processing, multiple access scheme, and networked control.

This paper focuses on the underdetermined blind source separation (BSS) of three speech signals mixed in a real environment from measurements provided by two sensors. To date, solutions to the underdetermined BSS problem have mainly been based on the assumption that the speech signals are sufficiently sparse. They involve designing binary masks that extract signals at time-frequency points where only one signal was assumed to exist. The major issue encountered in previous work relates to the occurrence of distortion, which affects a separated signal with loud musical noise. To overcome this problem, we propose combining sparseness with the use of an estimated mixing matrix. First, we use a geometrical approach to detect when only one source is active and to perform a preliminary separation with a time-frequency mask. This information is then used to estimate the mixing matrix, which allows us to improve our separation. Experimental results show that this combination of time-frequency mask and mixing matrix estimation provides separated signals of better quality (less distortion, less musical noise) than those extracted without using the estimated mixing matrix in reverberant conditions where the reverberant time (TR) was 130 ms and 200 ms. Furthermore, informal listening tests clearly show that musical noise is deeply lowered by the proposed method comparatively to the classical approaches.