We use compressed sensing to demonstrate theoretically the reconstruction of subwavelength features from measured far-field, and provide experimental proof-of-concept. The methods can be applied to non-optical microscopes, provided the information is sparse. A fundamental restriction of optical imaging is given by the diffraction limit, stating that the maximal recoverable resolution is set to half of the optical wavelength λ. This is a direct result of the evanescent nature of all plane-waves associated with spatial frequencies exceeding 1/λ [1]. Consequently, spatial frequencies higher than 1/λ are lost, even after short propagation distances of just a few wavelengths. Hence, using optical means to resolve subwavelength features from the far-field is virtually impossible. Reaching beyond the sub-wavelength barrier is a subject of intense research. A most useful approach is the Scanning Near-field Optical Microscope (SNOM) [2] which probes the EM field adjacent to the illuminated sample in the "near field" zone. Although the SNOM became a widely used method, its major draw back is the need to scan the sample point by point, preventing its use from real time applications. Alternatively, using the "hyperlens" made of negative-index metamaterials can transform the evanescent modes into propagating ones, enabling direct imaging of sub-wavelength information [3]. However, albeit offering a great promise, negative-index materials are currently severely restricted by high material loss, stringent fabrication requirements and the need to position them in the near-field of the sample. Distributing smallerthan-wavelength fluorescent particles on the sample, exciting them in various (linear and nonlinear) means, repeating the experiments multiple times and ensemble-averaging, constitutes another approach. But this method is not real-time either [4]. A more recent idea employs super-oscillations for sub-wavelength imaging, but this method still requires scanning, either in the near-field or in the plane where the super-oscillations are generated [5]. Apart from these "hardware solutions", several attempts have been made to extrapolate the frequency content above the cut-off frequency dictated by the diffraction limit. However, all of these extrapolation methods are extremely sensitive to noise in the measured data and the assumptions made on the prior knowledge on the information. As such, they have all failed in recovering optical sub-wavelength information [1]. Here, we show that sub-wavelength information can be recovered from the far-field of an optical image, with the only prior knowledge being that the image is sparse. The idea is based on recent compressed sensing (CS) techniques [6], which are generically used for efficient sampling of data. These methods are extremely robust to noise in the measured data. Their only condition is that the information is sparse. However, sparse optical images are common in nature, e.g., living cells, etc. We show theoretically the recovery of sub-wavelength structures from measured data restricted to the low spatial frequency content, and provide experimental proof-of-concept, recovering delicate features (amplitude and phase) that were cut off by spatial filtering. The underlying logic is that sparsely represented signals hold a very limited number of degrees of freedom, since only a small fraction of their coefficients (in the particular basis representation in which the signal is sparse) are non-zero. This enables to separate two subspaces of the basis functions: the one carrying information of our signal e while the other carries almost none. The aim of our approach is to automatically identify the first subspace and ignore the second. A key observation is that the reconstruction process corresponds to reconstructing a signal from the limited set of measurements from the low spatial frequencies. Hence, we need to compensate for the lost high spatial frequencies by assuming additional prior information on the signal, which is its sparsity. We define β as the sparsity level: the relative fraction of non-zero elements in the sparsifying basis of the signal. Since each nonzero component possesses two degrees of freedom – one for its location and the second for its amplitude, one should perform at least a 2β fraction of the total number of possible measurements, in order to reconstruct the signal. To gain more intuition in which basis the measurements should be preformed, let us consider measurements performed in the same basis in which the signal is sparse. Then, the vast majority of the measurements would be zero and cannot provide information about the true signal. In fact we would have to carry out almost all measurements in that basis in order to ensure exact reconstruction. Instead, we wish to choose the measurement basis such that each measurement of any projection contains information about the signal. This can be achieved by requiring that each measurement basis function has low correlation with each signal basis function. A highly uncorrelated pair of bases