## 1 Introduction  
Multispectral imaging systems obtain the spatial and spectral information of objects. They are widely used in material identification, object recognition, and other fields. There are already many different types of multispectral imaging techniques [1]. Conventional systems are implemented by optical narrowband filters or gratings to obtain different wavelengths. Due to their system complexity and high cost, most multispectral imagers are used and operated by researchers at laboratories. LED illumination-based multispectral imaging is a more practical system for the common consumer. Through the development of LED manufacturing technology, it has a fast switching ability and cost-effectiveness. Additionally, its structure is simple and without moving parts. It has been used in cultural heritage conservation [2], color reproduction [3], blood and melanin estimation [4], underwater surveys [5], etc. According to their illumination method, LED multispectral imaging systems can be classified into two major types. One typical type is the LED illumination in sequence system. In this type, different LEDs are illuminated in sequence and a camera captures images under every illumination. Further, either monochrome or RGB cameras can be used, and an optimal number of LEDs should be selected to reduce capturing times [6]. The other type is the multiplexed LED illumination system. Normally, several different LEDs are lit simultaneously, and an RGB camera is used to capture three-channel images in one shot [7,8]. This usually only needs two or three shots. In addition to these types, there are some other multiplexed LED illumination methods. For example, LEDs have been designed by using mutually orthogonal spectral functions as illuminations [9; 10]. This multiplexed method can easily obtain the reflection spectrum from captured images without optimal reconstruction, but it needs a higher number of LEDs and shots to obtain an accurate measurement. Besides being time-multiplexed, the illumination can be modulated by carrier frequency and transformed to the frequency domain [11]. This method can obtain high-quality multispectral images; however, it requires a signal generator to modulate the illumination, and requires many image sequences to demodulate the spectral images. The LED illumination in sequence system and the ordinary time-multiplexed method have simpler structures when compared to the orthogonal function and frequency modulation methods. However, spectral reconstruction is essential to recover spectral reflectance from the several obtained band images. Generally, the dimension of spectral reflectance is higher than the detected bands. The reconstruction process is an ill-posed inverse problem. Recently, many reconstruction methods have been introduced [12; 13], such as the Wiener [14], PCA [15], PLS [16], KPLS [17], NNMF [18; 19; 20], the machine learning algorithm [21; 22], and compressive sensing [23]. These methods are all effective for spectral reconstruction and continue to improve. The main purpose of improving these methods is to increase the accuracy of reconstruction. In this work, we focus on the computation time of reconstruction and introduce an efficient LED multispectral imaging system. The main contributions of this paper are reducing the time cost of reconstruction and maintaining a high accuracy. The following section will introduce the principle of our efficient multispectral imaging system. It has a typical LED illumination structure with an LED ring and an RGB camera. Further, an improved recovery method is presented to quickly reconstruct the multispectral images. In Section 3, the simulation results are analyzed to verify the reconstruction speed and spectral and spatial quality. This LED multispectral imaging system captures images quickly and obtains multispectral images in a timely fashion. Such a system is very suitable for human tongue detection in Chinese traditional medicine diagnosis.