Periodic boxcar deconvolution and diophantine approximation

By Iain M. Johnstone, Marc E. Raimondo. 2004

53 citations recorded by the source corpus.

We consider the nonparametric estimation of a periodic function that is observed in additive Gaussian white noise after convolution with a boxcar, the indicator function of an interval. This is an idealized model for the problem of recovery of noisy signals and images observed with motion blur. If the length of the boxcar is rational, then certain frequencies are irretreviably lost in the periodic model. We consider the rate of convergence of estimators when the length of the boxcar is irrational, using classical results on approximation of irrationals by continued fractions. A basic question of interest is whether the minimax rate of convergence is slower than for nonperiodic problems with 1/f-like convolution filters. The answer turns out to depend on the type and smoothness of functions being estimated in a manner not seen with homogeneous filters.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bff6062e2eb85429d9571a6ce70681e804111e3a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Jean-Pierre Florens
2. M. Carrasco
3. Karim Lounici
4. Richard Nickl
5. Xiaohong Chen
6. Sara A. van de Geer
7. D. Chetverikov
8. Evarist Gin'e

In Computer Vision and Pattern Recognition

1. Karim Lounici
2. Pablo J. Zarco-Tejada
3. Richard Nickl
4. Jean-Pierre Florens
5. Adam D. Bull
6. D. Chetverikov
7. Evarist Gin'e
8. Kolyan Ray

In Mathematical Physics

1. M. Carrasco
2. Karim Lounici
3. Richard Nickl
4. Jean-Pierre Florens
5. Ramon van Handel
6. Radosław Adamczak

Citations in the corpus

• A SPECTRAL METHOD FOR DECONVOLVING A DENSITY (2010, background): “This result is exploited in Johnstone and Raimondo (2004).”
• High-Throughput Estimation of Crop Traits: A Review of Ground and Aerial Phenotyping Platforms (2020, methodology): “2) A 5 × 5 boxcar filter is applied for screening and for the multilook to suppress speckle [286].”
• GLOBAL UNIFORM RISK BOUNDS FOR WAVELET DECONVOLUTION ESTIMATORS (2011, background): “It has been extensively studied: we refer to Carroll and Hall [9], Stefanski [37], Stefanski and Carroll [38], Fan [14, 15], Diggle and Hall [12], Goldenshluger [22], Pensky and Vidakovic [36], Delaigle and Gijbels [11], Hesse and Meister [24], Johnstone et al. [25], Johnstone and Raimondo [26], Bis”