Blind Compressed Sensing Over a Structured Union of Subspaces

This paper addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements. Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals come from a union of a small number of disjoint subspaces. This problem is important, for instance, in image inpainting applications, in which the multiple signals are constituted by (incomplete) image patches taken from the overall image. This work extends standard dictionary learning and block-sparse dictionary optimization, by considering compressive measurements, e.g., incomplete data). Previous work on blind compressed sensing is also generalized by using multiple sensing matrices and relaxing some of the restrictions on the learned dictionary. Drawing on results developed in the context of matrix completion, it is proven that both the dictionary and signals can be recovered with high probability from compressed measurements. The solution is unique up to block permutations and invertible linear transformations of the dictionary atoms. The recovery is contingent on the number of measurements per signal and the number of signals being sufficiently large; bounds are derived for these quantities. In addition, this paper presents a computationally practical algorithm that performs dictionary learning and signal recovery, and establishes conditions for its convergence to a local optimum. Experimental results for image inpainting demonstrate the capabilities of the method

Channel Estimation with Dynamic Metasurface Antennas via Model-Based Learning

Dynamic Metasurface Antenna (DMA) is a cutting-edge antenna technology offering scalable and sustainable solutions for large antenna arrays. The effectiveness of DMAs stems from their inherent configurable analog signal processing capabilities, which facilitate cost-limited implementations. However, when DMAs are used in multiple input multiple output (MIMO) communication systems, they pose challenges in channel estimation due to their analog compression. In this paper, we propose two model-based learning methods to overcome this challenge. Our approach starts by casting channel estimation as a compressed sensing problem. Here, the sensing matrix is formed using a random DMA weighting matrix combined with a spatial gridding dictionary. We then employ the learned iterative shrinkage and thresholding algorithm (LISTA) to recover the sparse channel parameters. LISTA unfolds the iterative shrinkage and thresholding algorithm into a neural network and trains the neural network into a highly efficient channel estimator fitting with the previous channel. As the sensing matrix is crucial to the accuracy of LISTA recovery, we introduce another data-aided method, LISTA-sensing matrix optimization (LISTA-SMO), to jointly optimize the sensing matrix. LISTA-SMO takes LISTA as a backbone and embeds the sensing matrix optimization layers in LISTA's neural network, allowing for the optimization of the sensing matrix along with the training of LISTA. Furthermore, we propose a self-supervised learning technique to tackle the difficulty of acquiring noise-free data. Our numerical results demonstrate that LISTA outperforms traditional sparse recovery methods regarding channel estimation accuracy and efficiency. Besides, LISTA-SMO achieves better channel accuracy than LISTA, demonstrating the effectiveness in optimizing the sensing matrix

Task-Driven Dictionary Learning

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited to restoration tasks. In this context, learning the dictionary amounts to solving a large-scale matrix factorization problem, which can be done efficiently with classical optimization tools. The same approach has also been used for learning features from data for other purposes, e.g., image classification, but tuning the dictionary in a supervised way for these tasks has proven to be more difficult. In this paper, we present a general formulation for supervised dictionary learning adapted to a wide variety of tasks, and present an efficient algorithm for solving the corresponding optimization problem. Experiments on handwritten digit classification, digital art identification, nonlinear inverse image problems, and compressed sensing demonstrate that our approach is effective in large-scale settings, and is well suited to supervised and semi-supervised classification, as well as regression tasks for data that admit sparse representations.Comment: final draft post-refereein

Dictionary Learning for Blind One Bit Compressed Sensing

This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix \Ab and sparse domain matrix $\Phi$, \ie \Db=\Ab\Phi, should be learned. Hence, we use dictionary learning to train this matrix. Towards that end, an appropriate continuous convex cost function is suggested for one bit compressed sensing and a simple steepest-descent method is exploited to learn the rows of the matrix \Db. Experimental results show the effectiveness of the proposed algorithm against the case of no dictionary learning, specially with increasing the number of training signals and the number of sign measurements.Comment: 5 pages, 3 figure

Communication channel analysis and real time compressed sensing for high density neural recording devices

Next generation neural recording and Brain- Machine Interface (BMI) devices call for high density or distributed systems with more than 1000 recording sites. As the recording site density grows, the device generates data on the scale of several hundred megabits per second (Mbps). Transmitting such large amounts of data induces significant power consumption and heat dissipation for the implanted electronics. Facing these constraints, efficient on-chip compression techniques become essential to the reduction of implanted systems power consumption. This paper analyzes the communication channel constraints for high density neural recording devices. This paper then quantifies the improvement on communication channel using efficient on-chip compression methods. Finally, This paper describes a Compressed Sensing (CS) based system that can reduce the data rate by > 10x times while using power on the order of a few hundred nW per recording channel