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In this paper, we provide two data-driven algorithms for learning compressive sensing measurement matrices with Gaussian entries. In contrast to the ubiquitous i.i.d.~Gaussian design, we associate different variances with different signal entries, so that we may utilize training data to focus more energy on the ``most important'' parts of the signal.

Analog-to-digital converters (ADCs) are known to suffer from saturation and clipping for inputs exceeding their dynamic range (DR). Recently, the Unlimited Sampling approach addressed this problem by inserting a modulo non-linearity between the input and the ADC. Moreover, a new model called modulo-hysteresis was introduced to enable the recovery of different classes of inputs from noisy observations. ADCs are typically assumed to acquire the instantaneous input amplitude via an inner product with a Dirac delta function.

The projection of sample measurements onto a reconstruction space represented by a basis on a regular grid is a powerful and simple approach to estimate a probability density function. In this paper, we focus on Riesz bases and propose a projection operator that, in contrast to previous works, guarantees the bona fide properties for the estimate, namely, non-negativity and total probability mass 1. Our bona fide projection is defined as a convex problem. We propose solution techniques and evaluate them.

The projection of sample measurements onto a reconstruction space represented by a basis on a regular grid is a powerful and simple approach to estimate a probability density function. In this paper, we focus on Riesz bases and propose a projection operator that, in contrast to previous works, guarantees the bona fide properties for the estimate, namely, non-negativity and total probability mass 1. Our bona fide projection is defined as a convex problem. We propose solution techniques and evaluate them.

Safe screening rules are powerful tools to accelerate iterative solvers in sparse regression problems. They allow early identification of inactive coordinates (i.e., those not belonging to the support of the solution) which can thus be screened out in the course of iterations. In this paper, we extend the GAP Safe screening rule to the L1-regularized Kullback-Leibler divergence which does not fulfill the regularity assumptions made in previous works. The proposed approach is experimentally validated on synthetic and real count data sets.

We address the problem of enabling two-dimensional digital image correlation (DIC) for strain measurement on large three-dimensional objects with curved surfaces. It is challenging to acquire full-field qualified images of the surface required by DIC due to geometric distortion and the narrow visual field of the surface that a single image can cover. To overcome this issue, we propose an end-to-end DIC framework incorporating the image fusion principle to achieve full-field strain measurement over the curved surface.

Turing computability deals with the question of what is theoretically computable on a digital computer, and hence is relevant whenever digital hardware is used. In this paper we study different possibilities to define computable bandlimited signals and systems. We consider a definition that uses finite Shannon sampling series as approximating functions and another that employs computable continuous functions together with an effectively computable time concentration. We discuss the advantages and drawbacks of both definitions and analyze the connections and differences.

Continuous-time Sigma-Delta modulators are oversampling Analog-to-Digital converters that may provide higher sampling rates and lower power consumption than their discrete counterpart. Whereas approximation errors are established for high-order discrete time Sigma-Delta modulators, theoretical analysis of the error between the filtered output and the input remain scarce.