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Optical interferometers provide multiple wavelength measurements. In order to fully exploit the spectral and spatial resolution of these instruments, new algorithms for image reconstruction have to be developed. Early attempts to deal with…
The theory of compressed sensing (CS) has been successfully applied to image compression in the past few years, whose traditional iterative reconstruction algorithm is time-consuming. However, it has been reported deep learning-based CS…
Used in the paper is an overcomplete piecewise-polynomial image model incorporating sparsity. The paper shows that using such a model, the edges in the image can be resolved robustly with respect to noise. Two variants of the proposed…
The mathematical theory of compressed sensing (CS) asserts that one can acquire signals from measurements whose rate is much lower than the total bandwidth. Whereas the CS theory is now well developed, challenges concerning hardware…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
Deep learning based image compressed sensing (CS) has achieved great success. However, existing CS systems mainly adopt a fixed measurement matrix to images, ignoring the fact the optimal measurement numbers and bases are different for…
Image segmentation is an inherently ill-posed problem and thus requires regularization in order to limit the search space to reasonable solutions. A majority of segmentation methods integrates these regularization terms in one way or the…
We provide two novel adaptive-rate compressive sensing (CS) strategies for sparse, time-varying signals using side information. Our first method utilizes extra cross-validation measurements, and the second one exploits extra low-resolution…
Standard deep learning models that employ the categorical cross-entropy loss are known to perform well at image classification tasks. However, many standard models thus obtained often exhibit issues like feature redundancy, low…
In recent years, compressed sensing (CS) has been applied in the field of synthetic aperture radar (SAR) imaging and shows great potential. The existing models are, however, based on application of the sensing matrix acquired by the exact…
Compressed sensing (CS) is a promising approach to reduce the number of measurements in photoacoustic tomography (PAT) while preserving high spatial resolution. This allows to increase the measurement speed and to reduce system costs.…
This paper provides an extension of compressed sensing which bridges a substantial gap between existing theory and its current use in real-world applications. It introduces a mathematical framework that generalizes the three standard…
The compressed sensing (CS) framework leverages the sparsity of MR images to reconstruct from undersampled acquisitions. CS reconstructions involve one or more regularization parameters that weigh sparsity in transform domains against…
Compressed sensing has empowered quality image reconstruction with fewer data samples than previously though possible. These techniques rely on a sparsifying linear transformation. The Daubechies wavelet transform is a common sparsifying…
We demonstrate that sub-wavelength optical images borne on partially-spatially-incoherent light can be recovered, from their far-field or from the blurred image, given the prior knowledge that the image is sparse, and only that. The…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…
This work reveals an experimental microscopy acquisition scheme successfully combining Compressed Sensing (CS) and digital holography in off-axis and frequency-shifting conditions. CS is a recent data acquisition theory involving signal…
The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate…
Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth…