We consider the problem of jointly recovering the vector b and the matrix C from noisy measurementsY=A(b)C+W , where A(⋅) is a known affine linear function of b (i.e., A(b)=A0 +∑Qi=1biAi with known matrices Ai ). This problem has applications in matrix completion, robust PCA, dictionary learning, self-calibration, blind deconvolution, joint-channel/symbol estimation, compressive sensing with matrix uncertainty, and many other tasks.

In this paper, we address the problem of recovering point sources from two-dimensional low-pass measurements, which is known as the super-resolution problem. This is the fundamental concern of many applications such as electronic imaging, optics, microscopy, and line spectral estimations. We assume that the point sources are located in the square [0,1]2 with unknown locations and complex amplitudes.

In this paper, we bridge the problem of (provably) learning shallow neural networks with the well-studied problem of low-rank matrix estimation. In particular, we consider two-layer networks with quadratic activations, and focus on the under-parameterized regime where the number of neurons in the hidden layer is smaller than the dimension of the input.

In this paper, we aim at designing sets of binary sequences with good aperiodic/periodic auto- and cross-correlation functions for multiple-input multiple-output (MIMO) radar systems. We show that such a set of sequences can be obtained by minimizing a weighted sum of peak sidelobe level (PSL) and integrated sidelobe level (ISL) with the binary element constraint at the design stage.