## 1 Introduction  
Hyperspectral imaging is a powerful tool for studying surface phenomena because hyperspectral sensors record hundreds of spectral bands that correspond to the components that make up the Earth's surface. Hyperspectral image (HSI) classification aims to categorize similar materials and objects, traditionally using conventional classifiers like random forests and support vector machines (SVMs) [1, 2]. However, due to the complex spectral behaviors of materials, these approaches based on spectral features often produce noisy results [3].  
To enhance HSI classification, the spatial/textural information of pixels can be incorporated [4]. Various spatial features, including Gabor textural features, morphological profiles, attribute profiles, superpixels, and local binary patterns, have been widely used for this purpose [3, 5, 6]. Fractal features (FFs) represent a robust textural measure extensively employed in various image-processing applications [7, 8]. Despite their considerable potential, FFs have yet to be thoroughly explored for remote-sensing HSI classification.  
Deep-learning methods, in particular the convolutional neural network (CNN), have attracted a lot of attention recently. In addition to conventional handcrafted spectral and spatial features, a CNN can consider spatial and spectral information simultaneously, proving its effectiveness in HSI classification [9, 10]. Additionally, certain studies have shown improved CNN performance by incorporating handcrafted spatial features alongside spectral features as inputs [11]. These advancements highlight the critical role of integrating multiple types of information to enhance the classification accuracy and robustness.  
Despite the existing body of research on the subject, there remains a need for simpler and more robust deep-learning approaches in HSI classification. To address this, our study aims to propose a novel deep-learning method named spectral-fractal iterative CNN (SF-ICNN) that leverages spectral and spatial information at different stages of the classification process. Our motivation arises from the demonstrated benefits of using spectral features along with two kinds of spatial information--one from FFs and the other from probability map (PM) images--in an iterative manner to enhance the performance of CNN classifiers. We hypothesize that CNNs can significantly improve performance by repeatedly utilizing PMs [12]. The key novelty of our proposed method lies in integrating these two types of spatial features (FFs and PMs), resulting in remarkable performance improvements in CNN-based HSI classification. The following are the suggested method's primary contributions:  
* The method combines FFs with spectral features as inputs to a CNN classifier. Experiments indicate that this novel strategy significantly enhances the classifier's performance.
* The method employs a novel combination of two types of spatial features, one from FFs and the other from PMs, iteratively to improve the CNN performance. This strategy enhances the classifier's performance statistically.
* Based on two benchmark HSI datasets, our experiment shows that the suggested deep-learning technique, with its more straightforward structure, outperforms certain state-of-the-art (SOTA) methods in terms of the classification accuracy within a reasonable processing time.  
Section 2 of our study includes a review of recent research pertinent to the topics we are studying. Section 3 consists of a detailed explanation of our proposed method for HSI classification. In Section 4, the HSI datasets that we used are introduced, and then the results of the experimental tests and comparisons are analyzed. Section 5 includes our concluding remarks.