## 1 Introduction  
White radish, as the second most common vegetable in China and a rich source of glucose, carotenoids, starch, and other nutrients, has been cultivated for thousands of years. It is mainly consumed in fresh and processed products and may be pickled or dried [1]. Black heart is an internal defect seen in postharvest radiishes which is due to lack of boron, waterlogging, anoxia in soil, and black rot during growth [2]. Generally, with this condition there are no obvious symptoms in the external appearance, but it is characterized by black dry rot in the medulla and the formation of voids. Although the white matter can be consumed when the diseased part is removed, the yield and quality declines greatly, and radish production has suffered serious losses as a result. Because the defects are internal, human visual inspection has limitations in evaluating the defects, which is time-consuming, subjective, and costly. Hence, an effective nondestructive inspection technology is valuable and necessary for efficient removal of defective rablishes before they enter the market. Many nondestructive sensing techniques, like spectroscopy, acoustics, and X-ray imaging, have been reported for internal quality inspection of fruits and vegetables [3; 4; 5; 6]. Among these methods, substantial work has focused on using near-infrared spectroscopy (NIRS) to inspect internal defects, like brown core in Chinese pears [7], brown heart in Braeburn apples [8; 9] and in Conference pears [10], translucent flesh disorder in mangosteen [11], black air-cavity defects in Japanese rablishes [12], and mealiness in apples [13]. Although NIRS is a fast, nondestructive, and effective method for measuring multiple quality attributes simultaneously [14], its measurement only gives an approximate quantification of the total light on a limited area and does not provide spatially resolved information. Hence, NIRS may not comprehensively evaluate internal defects in fruits and vegetables that may occur locally along the cavity [15]. Recently, hyperspectral imaging has entered wide use for evaluating the quality and safety of food and agricultural products [16; 17; 18]. Characterized as a rapid, nondestructive, and chemical-free method, hyperspectral imaging can simultaneously offer spatial information and spectral signals from one object, with the combination of conventional imaging and spectroscopy. The information obtained forms a three-dimensional data cube and can be processed to detect, identify, and quantify imaged objects in more detail than either traditional imaging or spectroscopic techniques [19]. Recently, considerable applications of hyperspectral imaging have been reported for the evaluation of internal quality in fruits and vegetables. For example, [PERSON] et al. [20] reported internal defect detection of cucumbers during pickling using hyperspectral imaging for real-time grading. Their previous studies also demonstrated the feasibility of detecting both external characteristics and internal defects of pickling cucumbers [15; 21]. [PERSON] et al. [22] conducted a study to detect cold injury in peaches. Based on the selected wavelengths and using an artificial neural network, 95.8% discrimination accuracy of chilled peaches was obtained. [PERSON] and [PERSON] [23] carried out apple mealiness detection using hyperspectral scattering imaging. Furthermore, quality attributes like soluble solids content, pH, and firmness can be successfully predicted by hyperspectral imaging [6; 24; 25; 26]. The technique, however, has so far been largely limited to laboratory or benchtop applications because of the cost, huge volume of data, and computing requirements. One way to solve these problems is to identify a few key discriminating wavelengths for real-time implementation and industrial applications, when the selected wavelengths contain approximately the same information as and/or are more efficient than full spectra [27; 28].