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We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements. Quantization, especially coarse quantization such as 1-bit sign measurements, leads to severe information loss and thus a good prior…
With quantum computing devices increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about quantum operations. However, current quantum devices are only capable of short…
In this paper we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. We present a new class of convex optimization programs, or decoders, coined Basis Pursuit DeQuantizer of moment $p$…
This paper presents a study on the reduction of the sampling frequency of the current signals of an induction motor, the reductions are performed by means time-decimation technique for digital signal processing. We have used the Fast…
The objective of quantitative photoacoustic tomography (QPAT) is to reconstruct optical and thermodynamic properties of heterogeneous media from data of absorbed energy distribution inside the media. There have been extensive theoretical…
The latest theoretical advances in the field of unlimited sampling framework (USF) show the potential to avoid clipping problems of analog-to-digital converters (ADC). To date, most of the related works have focused on real-valued modulo…
The problem of sampling a discrete-time sequence of spatially bandlimited fields with a bounded dynamic range, in a distributed, communication-constrained, processing environment is addressed. A central unit, having access to the data…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
This paper deals with the problem of reconstructing a band-limited signal when a finite subset of its samples and of its derivative are missing. The technique used, due to P.J.S.G. Ferreira, is based on the use of a particular frame for…
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is…
Channel simulation involves generating a sample $Y$ from the conditional distribution $P_{Y|X}$, where $X$ is a remote realization sampled from $P_X$. This paper introduces a novel approach to approximate Gaussian channel simulation using…
In Fourier-based medical imaging, sampling below the Nyquist rate results in an underdetermined system, in which linear reconstructions will exhibit artifacts. Another consequence of under-sampling is lower signal to noise ratio (SNR) due…
Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal -- sometimes greatly so. This paper develops generalized approximate message passing (GAMP) algorithms for…
In this thesis, I present several results on quantum statistical inference in the following two directions. Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a…
Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…
We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction…
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…
We consider the problem of sampling k-bandlimited graph signals, ie, linear combinations of the first k graph Fourier modes. We know that a set of k nodes embedding all k-bandlimited signals always exists, thereby enabling their perfect…
We show how real-number codes can be used to compress correlated sources, and establish a new framework for lossy distributed source coding, in which we quantize compressed sources instead of compressing quantized sources. This change in…
This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…