Related papers: Compressive Shift Retrieval
This note complements the paper "The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing" [2]. Its purpose is to present a proof of a result stated therein concerning the recovery…
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Compressed sensing is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution…
Compressed sensing (CS) demonstrates that a sparse, or compressible signal can be acquired using a low rate acquisition process below the Nyquist rate, which projects the signal onto a small set of vectors incoherent with the sparsity…
We present and study a scheme for lossless causal compression of periodic real-valued signals. In particular, our technique compresses a vector-valued signal to a scalar-valued signal by mixing it with another periodic signal. The…
Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
Suppose that a sequence of numbers $x_n$ (a `signal') is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations, $x_n + \xi_n$, where $\xi_n$ is a sequence of independent…
The promise of compressive sensing (CS) has been offset by two significant challenges. First, real-world data is not exactly sparse in a fixed basis. Second, current high-performance recovery algorithms are slow to converge, which limits CS…
In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods…
In this paper we study the general reconstruction of a compactly supported function from its Fourier coefficients using compactly supported shearlet systems. We assume that only finitely many Fourier samples of the function are accessible…
We describe an efficient, scalable Gaussian boson sampler based on a classical description of squeezed quantum light and a deterministic model of single-photon detectors that click when the incident amplitude falls above a given threshold.…
The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which…
Compressive sensing has been receiving a great deal of interest from researchers in many areas because of its ability in speeding up data acquisition. This framework allows fast signal acquisition and compression when signals are sparse in…
Suppose we wish to recover a signal x in C^n from m intensity measurements of the form |<x,z_i>|^2, i = 1, 2,..., m; that is, from data in which phase information is missing. We prove that if the vectors z_i are sampled independently and…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
The recently proposed modified-compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on…
We show that in the context of classification the property of source and target distributions to be related by covariate shift may be lost if the information content captured in the covariates is reduced, for instance by dropping components…
This paper presents modification of the TwIST algorithm for Compressive Sensing MRI images reconstruction. Compressive Sensing is new approach in signal processing whose basic idea is recovering signal form small set of available samples.…