Sharif Digital Repository

Matrix sensing refers to recovering a low-rank matrix from a few linear combinations of its entries. This problem naturally arises in many applications including recommendation systems, collaborative filtering, seismic data interpolation and wireless sensor networks. Recently, in these applications, it has been noted that exploiting additional subspace information might yield significant improvements in practical scenarios. This information is reflected by two subspaces forming angles with column and row spaces of the ground-truth matrix. Despite the importance of exploiting this information, there is limited theoretical guarantee for this feature. In this work, we aim to address this issue... 

With the dominance of digital imaging systems, we are often dealing with discrete-domain samples of an analog image. Due to physical limitations, all imaging devices apply a blurring kernel on the input image before taking samples to form the output pixels. In this paper, we focus on the reconstruction of binary shape images from few blurred samples. This problem has applications in medical imaging, shape processing, and image segmentation. Our method relies on representing the analog shape image in a discrete grid much finer than the sampling grid. We formulate the problem as the recovery of a rank $r$ matrix that is formed by a Hankel structure on the pixels. We further propose efficient... 

In this paper, we consider a multiple-input single-output (MISO) linear time-varying system whose output is a superposition of scaled and time-frequency shifted versions of inputs. The goal of this paper is to determine system characteristics and input signals from the single output signal. More precisely, we want to recover the continuous time-frequency shift pairs, the corresponding (complex-valued) amplitudes and the input signals from only one output vector. This problem arises in a variety of applications such as radar imaging, microscopy, channel estimation and localization problems. While this problem is naturally ill-posed, by constraining the unknown input waveforms to lie in... 

We consider the problem of corrupted radar super-resolution, a generalization of compressed radar super-resolution in which one aims to recover the continuous-valued delay-Doppler pairs of moving objects from a collection of corrupted and noisy measurements. The received signal in this type consists of contributions from objects, outlier and noise. While this problem is ill-posed in general, tractable recovery is possible when both the number of objects and corrupted measurements are limited. In this brief, we propose an atomic norm optimization in order to find the delay-Doppler pairs and the outlier signal. The objective function of our optimization problem encourages both sparsity in the...