In this paper, a new qualitative inverse scattering method for microwave imaging is proposed. The presented method is inspired by the previously introduced orthogonality sampling method (OSM) and direct sampling method (DSM), which aim to recover the reduced scattered fields. Both the OSM and the DSM are classified as backpropagation-based methods, and they are linked with the point source method and the linear sampling method. Although 3-D formulations of the OSM and the DSM exist for electromagnetic inverse scattering problems, the extension of these methods to near-field measurements is an open problem. The main contribution of this paper is introducing two novel linear operators to connect the reduced scattered fields and the tangential component of the scattered electric field measured on a circle for 2-D transverse electric (2-D-TE) and transverse magnetic (2-D-TM) inverse problems with the near-field measurements. To derive the kernel of these linear transformations, an integral equation is defined for each of the 2-D-TM and 2-D-TE problems. These equations are analytically solved, and the solutions are shown to be computable without any regularization. In addition to these theoretical contributions, the accuracy of the proposed approaches is shown with both numerical and experimental data. The constraints of the method are the measurement circle has to encover the scatterers and the targets have to be bounded in size and weak in contrast. The obtained results show that the developed approaches can be very useful in real-world applications, such as nondestructive testing and biomedical imaging.