Joint-2D-SL0 Algorithm for Joint Sparse Matrix Reconstruction

Sparse matrix reconstruction has a wide application such as DOA estimation and STAP. However, its performance is usually restricted by the grid mismatch problem. In this paper, we revise the sparse matrix reconstruction model and propose the joint sparse matrix reconstruction model based on one-order Taylor expansion. And it can overcome the grid mismatch problem. Then, we put forward the Joint-2D-SL0 algorithm which can solve the joint sparse matrix reconstruction problem efficiently. Compared with the Kronecker compressive sensing method, our proposed method has a higher computational efficiency and acceptable reconstruction accuracy. Finally, simulation results validate the superiority of the proposed method

Signal Recovery in Perturbed Fourier Compressed Sensing

In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of measurements. However due to system calibration errors, the system may measure the Fourier transform at frequencies $\{u_i + \delta_i\}_{i=1}^M$ that are different from the base frequencies and where $\{\delta_i\}_{i=1}^M$ are unknown. Ignoring perturbations of this nature can lead to major errors in signal recovery. In this paper, we present a simple but effective alternating minimization algorithm to recover the perturbations in the frequencies \emph{in situ} with the signal, which we assume is sparse or compressible in some known basis. In many cases, the perturbations $\{\delta_i\}_{i=1}^M$ can be expressed in terms of a small number of unique parameters $P \ll M$. We demonstrate that in such cases, the method leads to excellent quality results that are several times better than baseline algorithms (which are based on existing off-grid methods in the recent literature on direction of arrival (DOA) estimation, modified to suit the computational problem in this paper). Our results are also robust to noise in the measurement values. We also provide theoretical results for (1) the convergence of our algorithm, and (2) the uniqueness of its solution under some restrictions.Comment: New theortical results about uniqueness and convergence now included. More challenging experiments now include

Joint Image and Depth Estimation With Mask-Based Lensless Cameras

Mask-based lensless cameras replace the lens of a conventional camera with a custom mask. These cameras can potentially be very thin and even flexible. Recently, it has been demonstrated that such mask-based cameras can recover light intensity and depth information of a scene. Existing depth recovery algorithms either assume that the scene consists of a small number of depth planes or solve a sparse recovery problem over a large 3D volume. Both these approaches fail to recover the scenes with large depth variations. In this paper, we propose a new approach for depth estimation based on an alternating gradient descent algorithm that jointly estimates a continuous depth map and light distribution of the unknown scene from its lensless measurements. We present simulation results on image and depth reconstruction for a variety of 3D test scenes. A comparison between the proposed algorithm and other method shows that our algorithm is more robust for natural scenes with a large range of depths. We built a prototype lensless camera and present experimental results for reconstruction of intensity and depth maps of different real objects