COVID-19 is a novel virus, which has a fast spreading rate, and now it is seen all around the world. The case and death numbers are increasing day by day. Some tests have been used to determine the COVID-19. Chest X-ray and chest computerized tomography (CT) are two important imaging tools for determination and monitoring of COVID-19. And new methods have been searching for determination of the COVID-19. In this paper, the investigation of various multiresolution approaches in detection of COVID-19 is carried out. Chest X-ray images are used as input to the proposed approach. As recent trend in machine learning shifts toward the deep learning, we would like to show that the traditional methods such as multiresolution approaches are still effective. To this end, the well-known multiresolution approaches namely Wavelet, Shearlet and Contourlet transforms are used to decompose the chest X-ray images and the entropy and the normalized energy approaches are employed for feature extraction from the decomposed chest X-ray images. Entropy and energy features are generally accompanied with the multiresolution approaches in texture recognition applications. The extreme learning machines (ELM) classifier is considered in the classification stage of the proposed study. A dataset containing 361 different COVID-19 chest X-ray images and 200 normal (healthy) chest X-ray images are used in the experimental works. The performance evaluation is carried out by employing various metric namely accuracy, sensitivity, specificity and precision. As deep learning is mentioned, a comparison between proposed multiresolution approaches and deep learning approaches is also carried out. To this end, deep feature extraction and fine-tuning of pretrained convolutional neural networks (CNNs) are considered. For deep feature extraction, pretrained, ResNet50 model is employed. For classification of the deep features, the Support Vector Machines (SVM) classifier is used. The ResNet50 model is also used in the fine-tuning. The experimental works show that multiresolution approaches produced better performance than the deep learning approaches. Especially, Shearlet transform outperformed at all. 99.29% accuracy score is obtained by using Shearlet transform.