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In many particle physics experiments the data processing is based on the analysis of the digitized waveforms provided by the detector. While the waveform amplitude is usually correlated to the event energy, the shape may carry useful…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
High-resolution array detectors are widely used in single-particle tracking, but their performance is limited by excess noise from background light and dark current. As pixel resolution increases, the diminished signal per pixel exacerbates…
Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the…
Successful wavelet estimation is an essential step for seismic methods like impedance inversion, analysis of amplitude variations with offset and full waveform inversion. Homomorphic deconvolution has long intrigued as a potentially elegant…
Reconstruction-based anomaly detection via denoising diffusion model has limitations in determining appropriate noise parameters that can degrade anomalies while preserving normal characteristics. Also, normal regions can fluctuate…
Image blur and image noise are imaging artifacts intrinsically arising in image acquisition. In this paper, we consider multi-frame blind deconvolution (MFBD), where image blur is described by the convolution of an unobservable,…
In this work, we address the challenging problem of blind deconvolution for color images. Existing methods often convert color images to grayscale or process each color channel separately, which overlooking the relationships between color…
This article describes a fast iterative algorithm for image denoising and deconvolution with signal-dependent observation noise. We use an optimization strategy based on variable splitting that adapts traditional Gaussian noise-based…
In this paper, we propose a Bayesian MAP estimator for solving the deconvolution problems when the observations are corrupted by Poisson noise. Towards this goal, a proper data fidelity term (log-likelihood) is introduced to reflect the…
Patient scans from MRI often suffer from noise, which hampers the diagnostic capability of such images. As a method to mitigate such artifact, denoising is largely studied both within the medical imaging community and beyond the community…
Deep Learning based methods have emerged as the indisputable leaders for virtually all image restoration tasks. Especially in the domain of microscopy images, various content-aware image restoration (CARE) approaches are now used to improve…
Richardson-Lucy deconvolution is widely used to restore images from degradation caused by the broadening effects of a point spread function and corruption by photon shot noise, in order to recover an underlying object. In practice, this is…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
We consider the problem of denoising a function observed after a convolution with a random filter independent of the noise and satisfying some mean smoothness condition depending on an ill posedness coefficient. We establish the minimax…
X-ray spectral fitting of astronomical sources requires convolving the intrinsic spectrum or model with the instrumental response. Standard forward modeling techniques have proven success in recovering the underlying physical parameters in…
We introduce a new audio processing technique that increases the sampling rate of signals such as speech or music using deep convolutional neural networks. Our model is trained on pairs of low and high-quality audio examples; at test-time,…
Ultrasound imaging serves as an effective and non-invasive diagnostic tool commonly employed in clinical examinations. However, the presence of speckle noise in ultrasound images invariably degrades image quality, impeding the performance…
Radio synthesis imaging is dependent upon deconvolution algorithms to counteract the sparse sampling of the Fourier plane. These deconvolution algorithms find an estimate of the true sky brightness from the necessarily incomplete sampled…