Coronavirus disease (COVID-19) has been the main agenda of the whole world ever since it came into sight. X-ray imaging is a common and easily accessible tool that has great potential for COVID-19 diagnosis and prognosis. Deep learning techniques can generally provide state-of-the-art performance in many classification tasks when trained properly over large data sets. However, data scarcity can be a crucial obstacle when using them for COVID-19 detection. Alternative approaches such as representation-based classification [collaborative or sparse representation (SR)] might provide satisfactory performance with limited size data sets, but they generally fall short in performance or speed compared to the neural network (NN)-based methods. To address this deficiency, convolution support estimation network (CSEN) has recently been proposed as a bridge between representation-based and NN approaches by providing a noniterative real-time mapping from query sample to ideally SR coefficient support, which is critical information for class decision in representation-based techniques. The main premises of this study can be summarized as follows: 1) A benchmark X-ray data set, namely QaTa-Cov19, containing over 6200 X-ray images is created. The data set covering 462 X-ray images from COVID-19 patients along with three other classes; bacterial pneumonia, viral pneumonia, and normal. 2) The proposed CSEN-based classification scheme equipped with feature extraction from state-of-the-art deep NN solution for X-ray images, CheXNet, achieves over 98% sensitivity and over 95% specificity for COVID-19 recognition directly from raw X-ray images when the average performance of 5-fold cross validation over QaTa-Cov19 data set is calculated. 3) Having such an elegant COVID-19 assistive diagnosis performance, this study further provides evidence that COVID-19 induces a unique pattern in X-rays that can be discriminated with high accuracy.