Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1808.06942

PACO: Global Signal Restoration via PAtch COnsensus

Ignacio Francisco Ramírez Paulino
View original source ↗Read source document ↗Export metadata ↓

Abstract

Many signal processing algorithms break the target signal into overlapping segments (also called windows, or patches), process them separately, and then stitch them back into place to produce a unified output. At the overlaps, the final value of those samples that are estimated more than once needs to be decided in some way. Averaging, the simplest approach, often leads to unsatisfactory results. Significant work has been devoted to this issue in recent years. Several works explore the idea of a weighted average of the overlapped patches and/or pixels; others promote agreement (consensus) between the patches at their intersections. Agreement can be either encouraged or imposed as a hard constraint. This work develops on the latter case. The result is a variational signal processing framework, named PACO, which features a number of appealing theoretical and practical properties. The PACO framework consists of a variational formulation that fits a wide variety of problems, and a general ADMMbased algorithm for minimizing the resulting energies. As a byproduct, we show that the consensus step of the algorithm, which is the main bottleneck of similar methods, can be solved efficiently and easily for any arbitrary patch decomposition scheme. We demonstrate the flexibility and power of PACO on three different problems: image inpainting (which we have already covered in previous works), image denoising, and contrast enhancement, using different cost functions including Laplacian and Gaussian Mixture Models.

Explore related subjects

eess.SPcs.DCcs.LGcs.NAmath.NAstat.ML

Keep this discovery

BibTeXRIS

Ignacio Francisco Ramírez Paulino. 2018-08-20. PACO: Global Signal Restoration via PAtch COnsensus. https://arxiv.org/abs/1808.06942

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Load Balancing in Multi-Shell LEO Satellite Networks with Successive Interference Cancellation

Multi-shell low Earth orbit (LEO) networks can increase service opportunities, but altitude-dependent propagation can concentrate traffic on lower shells and create strong inter-shell interference under full frequency reuse. This paper develops a mathematical framework for load balancing in multi-shell LEO satellite networks. Satellites on each shell form an independent spherical Poisson point process (SPPP), and the typical user associates with one of the per-shell serving satellites through a shell-dependent biased received-power rule, with receiver-side successive interference cancellation (SIC) under full frequency reuse. Shell-wise association probabilities, conditioned serving-distance distributions, and the rate coverage probability under shell-dependent traffic loads are derived and validated by simulation. The results show that shell-dependent biasing alleviates lower-shell traffic concentration and improves rate coverage, while receiver-side SIC mitigates the dominant lower-shell interference experienced by users associated with upper shells. Load balancing provides its largest rate-coverage gain in traffic hotspots, while SIC becomes more valuable as receive-side isolation weakens. With a fixed satellite budget, distributing satellites across multiple shells can further improve hotspot rate coverage by adding shell-wise serving opportunities.

eess.SP↗
arXiv2026

Tensor Decomposition Based Mixed-Field Sensing for XL-MIMO AFDM Systems

Integrated sensing and communications enabled by extremely large-scale MIMO (XL-MIMO) and affine frequency division multiplexing (AFDM) is a highly promising paradigm for vehicular networks. However, the near-field spherical wavefront distortions induce severe non-linear parameter coupling, while the highly dynamic scattering environments exacerbate mismatch errors. To address these critical challenges, this paper proposes a novel tensor-based sensing scheme for XL-MIMO AFDM systems. First, the received signals are reformulated into a tensor, followed by an efficient decomposition approach that exploits the inherent Vandermonde structure of the factor matrices. This allows parameters to be directly estimated from the decomposed matrices, effectively avoiding inter-parameter coupling. Subsequently, a symmetric decoupling and real-domain manifold optimization algorithm is proposed for angle of arrival estimation, circumventing the high-dimensional searches typically induced by near-field effects. Furthermore, a baseband reconstruction and analytical gradient-based algorithm is developed to perform delay-Doppler estimation in the continuous parameter domain, fundamentally eradicating the grid-mismatch errors inherent in high-mobility scenarios. With these decoupled factors, the remaining unknown angle of departure can be readily extracted. Extensive simulation results demonstrate that the proposed scheme achieves orders-of-magnitude improvements in delay-Doppler accuracy and eliminates the error floors in angular estimation that severely bottleneck state-of-the-art baselines.

eess.SP↗
arXiv2026

Radio Map Construction with Post-Hoc Location Calibration under Quasi-Static Positioning Errors: Joint Estimation, Performance Bounds, and GNSS-Based Evaluation

Radio maps enable environment-aware wireless and Internet-of-Things applications and can be constructed from location-tagged received signal strength (RSS) measurements collected by mobile devices. In urban environments, temporally correlated GNSS errors can shift an entire sensing trajectory, causing systematic spatial misregistration that is not mitigated by collecting more measurements. This paper presents a radio-map construction framework that uses the radio measurements themselves to calibrate erroneous location tags after data collection. The dominant positioning error is modeled as a sensor-specific quasi-static offset, which is jointly estimated with radio-propagation parameters in a Gaussian process regression (GPR) framework by exploiting complementary spatial information from distance-dependent path loss and spatially correlated shadowing. We establish lower and upper bounds on the conditional Bayes risk and show that, under a translation-invariant trajectory model, trajectory information alone cannot identify the quasi-static offset, thereby motivating the use of RSS-derived spatial information for calibration. Numerical evaluations across propagation conditions show that the proposed method reduces the mean squared error (MSE) gap from ideal GPR to approximately $3.26\mathrm{dB}^2$, compared with about $10\mathrm{dB}^2$ for position-error-agnostic and noisy-input GPR baselines. Evaluation using positioning-error models derived from smartphone GNSS measurements shows that the proposed method outperforms a KF--RTS trajectory-smoothing baseline despite unmodeled time-varying positioning errors, remaining within approximately $5\mathrm{dB}^2$ of ideal GPR at the median MSE. These results demonstrate that RSS measurements can serve not only as observations for radio-map reconstruction but also as spatial cues for post-hoc calibration of imperfectly geotagged sensing data.

eess.SP↗