A method for magnetic resonance imaging (MRI) is investigated here, whereby an object is put under a homogeneous magnetic field, and the image is obtained by applying inverse source procedures to the data collected in an array of coil detectors surrounding the object. The induced current in each coil due to the precession of the magnetic dipole in each voxel depends on the characteristics of both the magnetic dipole frequency and strength, together with its distance from the coil, the coil direction in space, and the electrical properties of the coils. By calculating the induced current signals over an array of coil detectors, a relationship is established between the set of signals and the structure of the body under investigation. The linear relation can then be represented in matrix notation, and inversion of this matrix will produce an image of the body. Important problems which must be considered in the proposed method are signal-to-noise ratio (SNR) and coupling between adjacent coils. Solutions to these problems will provide a new method for obtaining an instantaneous image by NMR, with no need for gradient switching for encoding. A general algorithm for decoupling of the coils is presented and fast sampling of the signal, instead of filtering, is used in order to reduce both noise and numerical roundoff errors at the same time. Sensitivity considerations are made with respect to the number of coils that is required and its connection with coil radius and SNR. A computer simulation demonstrates the feasibility of this new modality. Based on the solutions presented here for the problems involved in the use of a large number of coils for a simultaneous recording of the signal, an improved method of multicoil recording is suggested, whereby it is combined with the conventional zeugmatographic method with read and phase gradients, to result in a novel method of magnetic resonance imaging. In the combined method, there are no phase-encoding gradients. Only a single slice-selecting gradient, to be followed by a single read-gradient. Instead of phase-encoding gradients, use is made of an equivalent number of coils. The number of coils now is reduced significantly. This method suggests a single slice image taken within a single echo time, and where a 128 x 128 resolution is possible with only 128 coils. The applicability of the method is based on a successful decoupling procedure for the detectors (coils and cables) and the availability of highly accurate, high-gain, low-noise amplifiers with a broad dynamic range.