Learning-Based Compressive Subsampling

Abstract

The problem of recovering a structured signal x ∈ C p from a set of dimensionality-reduced linear measurements b = Ax arises in a variety of applications, such as medical imaging, spectroscopy, Fourier optics, and computerized tomography. Due to computational and storage complexity or physical constraints imposed by the problem, the measurement matrix A ∈ C n×p is often of the form A = PΩΨ for some orthonormal basis matrix Ψ ∈ C p×p and subsampling operator PΩ : C p → C n that selects the rows indexed by Ω. This raises the fundamental question of how best to choose the index set Ω in order to optimize the recovery performance. Previous approaches to addressing this question rely on non-uniform random subsampling using application-specific knowledge of the structure of x. In this paper, we instead take a principled learning-based approach in which a fixed index set is chosen based on a set of training signals x1, . . . , xm. We formulate combinatorial optimization problems seeking to maximize the energy captured in these signals in an average-case or worst-case sense, and we show that these can be efficiently solved either exactly or approximately via the identification of modularity and submodularity structures. We provide both deterministic and statistical theoretical guarantees showing how the resulting measurement matrices perform on signals differing from the training signals, and we provide numerical examples showing our approach to be effective on a variety of data sets.

DCT Learning-Based Hardware Design for Neural Signal Acquisition Systems

“…The LBCS method [11] consists on linear encoding and linear decoding with respect to a given orthonormal basis, resulting in a much simpler and faster solution compared to standard CS. LBCS can be summarized as follows.…”

“…are the largest [11]. The learnt sampling scheme is then used to directly sample only those transform coefficients indexed byΩ for all signals x.…”

Learning-Based Near-Optimal Area-Power Trade-offs in Hardware Design for Neural Signal Acquisition

“…The compression architecture that we propose in this paper is based on the idea of Learning-Based Compressive Subsampling (LBCS) [9], which consists on linear encoding and linear decoding with respect to a given orthonormal basis, resulting in a much simpler and faster solution compared to the approaches described in Section 2.1.…”

“…are the largest [9]. The learnt sampling scheme is then used to directly sample only those transform coefficients indexed byΩ for all signals x.…”

“…In this work, we design a digital encoder for neuronal signals based on Learning Based Compressive Subsampling (LBCS) [9], which allows to reduce the chip's power and area requirements, while improving on the reconstruction performance. Such method is based on the simple idea of sampling a fixed set of coefficients that preserve as much of the signal's energy as possible.…”