7,396 research outputs found
A Simple Message-Passing Algorithm for Compressed Sensing
We consider the recovery of a nonnegative vector x from measurements y = Ax,
where A is an m-by-n matrix whos entries are in {0, 1}. We establish that when
A corresponds to the adjacency matrix of a bipartite graph with sufficient
expansion, a simple message-passing algorithm produces an estimate \hat{x} of x
satisfying ||x-\hat{x}||_1 \leq O(n/k) ||x-x(k)||_1, where x(k) is the best
k-sparse approximation of x. The algorithm performs O(n (log(n/k))^2 log(k))
computation in total, and the number of measurements required is m = O(k
log(n/k)). In the special case when x is k-sparse, the algorithm recovers x
exactly in time O(n log(n/k) log(k)). Ultimately, this work is a further step
in the direction of more formally developing the broader role of
message-passing algorithms in solving compressed sensing problems
Approximate Message Passing with Restricted Boltzmann Machine Priors
Approximate Message Passing (AMP) has been shown to be an excellent
statistical approach to signal inference and compressed sensing problem. The
AMP framework provides modularity in the choice of signal prior; here we
propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a
Restricted Boltzmann Machine (RBM) trained on the signal support to push
reconstruction performance beyond that of simple iid priors for signals whose
support can be well represented by a trained binary RBM. We present and analyze
two methods of RBM factorization and demonstrate how these affect signal
reconstruction performance within our proposed algorithm. Finally, using the
MNIST handwritten digit dataset, we show experimentally that using an RBM
allows AMP to approach oracle-support performance
Grant-Free Massive MTC-Enabled Massive MIMO: A Compressive Sensing Approach
A key challenge of massive MTC (mMTC), is the joint detection of device
activity and decoding of data. The sparse characteristics of mMTC makes
compressed sensing (CS) approaches a promising solution to the device detection
problem. However, utilizing CS-based approaches for device detection along with
channel estimation, and using the acquired estimates for coherent data
transmission is suboptimal, especially when the goal is to convey only a few
bits of data.
First, we focus on the coherent transmission and demonstrate that it is
possible to obtain more accurate channel state information by combining
conventional estimators with CS-based techniques. Moreover, we illustrate that
even simple power control techniques can enhance the device detection
performance in mMTC setups.
Second, we devise a new non-coherent transmission scheme for mMTC and
specifically for grant-free random access. We design an algorithm that jointly
detects device activity along with embedded information bits. The approach
leverages elements from the approximate message passing (AMP) algorithm, and
exploits the structured sparsity introduced by the non-coherent transmission
scheme. Our analysis reveals that the proposed approach has superior
performance compared to application of the original AMP approach.Comment: Submitted to IEEE Transactions on Communication
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