For instance, for an overwhelming number of real images, appropriate transforms such as DCT compact the image energy into the lower frequency part of spectral components. It is this property that is put in the base of transform coefficient zonal quantization tables in transform image coding such as JPEG. Therefore, one can, in addition to specifying the number $N$ of desired images samples and the number $M$ of samples to be taken, which is required by the CS approach, make a natural assumption that the image spectral components important for image reconstruction are concentrated within, say, a circular shape that encompasses $M$ spectral components with the lowest indices. With this assumption, one can either sample the image in a regular way with a sampling rate defined by dimensions of a square that circumscribes this shape or, more efficiently in terms of reducing the required number of samples, reconstruct an image sparse approximation from a set of $M$ samples taken, in the case of sparsity of DCT or DFT spectra, in randomly chosen positions. For the reconstruction, an iterative Gershberg–Papoulis type algorithm can be employed.^{10} This option [let us call it random sampling and band limited reconstruction (RSBLR)], is illustrated in Fig. 3 on an example of a test image “Ango” from a set of 11 test images listed in Table 2.