Related papers: Information theoretic bounds for Compressed Sensin…
For several styles of fidelity constraints -- guaranteed distortion, conditional excess distortion, excess distortion -- we show mutual information upper bounds on the minimum expected description length needed to represent a random…
Consider the noisy underdetermined system of linear equations: y=Ax0 + z0, with n x N measurement matrix A, n < N, and Gaussian white noise z0 ~ N(0,\sigma^2 I). Both y and A are known, both x0 and z0 are unknown, and we seek an…
Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. This line of work shows that $\ell_1$-regularized…
Compressed sensing provides an efficient framework for reconstructing wave signals from reduced measurements. For multi-channel buoy data, the three displacement components exhibit intrinsic correlations, as wave motion contributes…
We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a…
Reconstructive spectrometers are a promising emerging class of devices that combine complex light scattering with inference to enable compact, high-resolution spectrometry. Thus far, the physical determinants of these devices' performance…
In this work, we study the problem of reconstructing a sparse signal from a limited number of linear 'incoherent' noisy measurements, when a part of its support is known. The known part of the support may be available from prior knowledge…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…
Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or…
We present a novel systematic theoretical framework to analyze the rate-distortion (R-D) limits of learned image compression. While recent neural codecs have achieved remarkable empirical results, their distance from the…
The article concerns compressed sensing methods in the quaternion algebra. We prove that it is possible to uniquely reconstruct - by $\ell_1$ norm minimization - a sparse quaternion signal from a limited number of its real linear…
We consider in this paper the problem of estimating a parameter matrix from observations which are affected by two types of noise components: (i) a sparse noise sequence which, whenever nonzero can have arbitrarily large amplitude (ii) and…
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
In this paper, we study the number of measurements required to recover a sparse signal in ${\mathbb C}^M$ with $L$ non-zero coefficients from compressed samples in the presence of noise. For a number of different recovery criteria, we prove…
Periodic signals composed of periodic mixtures admit sparse representations in nested periodic dictionaries (NPDs). Therefore, their underlying hidden periods can be estimated by recovering the exact support of said representations. In this…
Conventional compressed sensing theory assumes signals have sparse representations in a known, finite dictionary. Nevertheless, in many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…