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With the rapid growth of data, how to extract effective information from data is one of the most fundamental problems. In this paper, based on Tikhonov regularization, we propose an effective method for reconstructing the function and its…

Counting objects in digital images is a process that should be replaced by machines. This tedious task is time consuming and prone to errors due to fatigue of human annotators. The goal is to have a system that takes as input an image and…

Representing a continuous-time signal by a set of samples is a classical problem in signal processing. We study this problem under the additional constraint that the samples are quantized or compressed in a lossy manner under a limited…

Image resampling is a necessary component of any operation that changes the size of an image or its geometry. Methods tuned for natural image upsampling (roughly speaking, image enlargement) are analyzed and developed with a focus on their…

In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…

Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a…

We provide a theoretical justification for sample recovery using diffusion based image inpainting in a linear model setting. While most inpainting algorithms require retraining with each new mask, we prove that diffusion based inpainting…

In many applications of tomography, the acquired projections are either limited in number or contain a significant amount of noise. In these cases, standard reconstruction methods tend to produce artifacts that can make further analysis…

A hardware architecture for the single iteration algorithm is proposed in this paper. Single iteration algorithm enables reconstruction of the full signal when small number of signal samples is available. The algorithm is based on the…

Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions…

As technology grows, higher frequency signals are required to be processed in various applications. In order to digitize such signals, conventional analog to digital convertors are facing implementation challenges due to the higher sampling…

The goal of this paper is to present a non-iterative and more importantly an extremely fast algorithm to reconstruct images from compressively sensed (CS) random measurements. To this end, we propose a novel convolutional neural network…

We present a simple and efficient Bayesian recursive algorithm for the data-pattern scheme for quantum state reconstruction, which is applicable to situations where measurement settings can be controllably varied efficiently. The algorithm…

Image-generative artificial intelligence (AI) has garnered significant attention in recent years. In particular, the diffusion model, a core component of generative AI, produces high-quality images with rich diversity. In this study, we…

We address the problem of sparse recovery in an online setting, where random linear measurements of a sparse signal are revealed sequentially and the objective is to recover the underlying signal. We propose a reweighted least squares (RLS)…

Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…

Remotely generated data by Intent of Things (IoT) has recently had a lot of attention for their huge benefits such as efficient monitoring and risk reduction. The transmitted streams usually consist of periodical streams (e.g. activities)…

With distributed machine learning being a prominent technique for large-scale machine learning tasks, communication complexity has become a major bottleneck for speeding up training and scaling up machine numbers. In this paper, we propose…

A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…

Upon compressing perceptually relevant signals, conventional quantization generally results in unnatural outcomes at low rates. We propose distribution preserving quantization (DPQ) to solve this problem. DPQ is a new quantization concept…