In this era of Coronavirus disease 2019 (COVID-19), an accurate method of diagnosis with less diagnosis time and cost can effectively help in controlling the disease spread with the new variants taking birth from time to time. In order to achieve this, a two-dimensional (2D) tunable Q-wavelet transform (TQWT) based on a memristive crossbar array (MCA) is introduced in this work for the decomposition of chest X-ray images of two different datasets. TQWT has resulted in promising values of peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) at the optimum values of its parameters namely quality factor (Q) of 4, and oversampling rate (r) of 3 and at a decomposition level (J) of 2. The MCA-based model is used to process decomposed images for further classification with efficient storage. These images have been further used for the classification of COVID-19 and non-COVID-19 images using ResNet50 and AlexNet convolutional neural network (CNN) models. The average accuracy values achieved for the processed chest X-ray images classification in the small and large datasets are 98.82% and 94.64%, respectively which are higher than the reported conventional methods based on different models of deep learning techniques. The average accuracy of detection of COVID-19 via the proposed method of image classification has also been achieved with less complexity, energy, power, and area consumption along with lower cost estimation as compared to CMOS-based technology. •Qualitative and quantitative investigations on selection of optimum TQWT parameters for image decomposition.•Extended mathematical investigation for memristive crossbar array (MCA) model based two dimensional (2D) TQWT to decompose the CXIs for further image classification.•Computational diagnosis of COVID-19 by using CXIs through pretrained CNN models.