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Qualitative inverse scattering methods have been a subject of much interest in the inverse scattering community for the past two decades. In contrast to image reconstruction methods, such as the celebrated back-projection methods,qualitative methods do not rely on weak scattering approximations and are thus appropriate for multiple scattering imaging. In particular the most well established of these methods known as the Linear Sampling Method is based on solving a certain linear and ill-posed integral equation. Thus for sufficiently dense and large enough aperture viewing angles the method promotes promotes simplicity,speed, and good qualityreconstructions. The main drawback of this method is the assumption of complete redundant multi-static data. In practice however, such data might not be possible or perhaps too costly to obtain. An example of such a case would be in the field of radar imaging, where increasing the number of sensors also increases the likelihood of enemy detection.Our work is based on LSM imaging with radar imaging as the main target application. Specifically we deal with the case of sparse and/or aperture obstacle scattering. We attempt to improve the reconstruction quality for thesesituations by focusing on introducing physically meaningful constraints into the regularization of the so called far-field equation. The first portion of our study focused on constraining our desired solutions to those that exhibit sparse spatial gradients. The second portion of our proposed study is focused on multi-frequency LSM. The LSM method is primarily a single frequency approach, to our knowledge very little work exists on exploiting multi-frequencydata within the LSM framework. We show that solutions to the far-field equation exhibit a Lipschitz like continuity with respect to frequency. We develop a frequency based regularization method that exploits this a priori knowledge.