Prof. Thierry Blu
FIEEE, FHKIE
News
Demos/Softwares
Design of Orthonormal Rational Filter Banks
A Matlab implementation of the algorithm described in this paper: download the zip archive.
These filters are used to build a non-dyadic (fractional) multiresolution analysis corresponding to some kind of wavelet decomposition that corresponds to a fraction-of-octave analysis (e.g., scaling factor = 6/5 to mimick a Bark-scale decomposition). See my PhD thesis (in French) for the most complete account of this research.
Fractional Spline Wavelet transform
A Matlab implementation of the DWT algorithm described in this paper using fractional spline filters defined in this paper: download the zip archive.
This algorithm implements a continuously defined family of scaling/wavelet filters specified with two parameters: the degree of the spline (which conditions its support and approximation order) and its "shift".
More details...Fast Computation of the 3D PSF of a Microscope
A Matlab implementation of the algorithm described in this paper and that computes Gibson-Lanni's integral expression: download the zip archive.
More details...?URE-LET Image Denoising
Matlab implementations of the various ?URE-LET (currently: ? = S, P or C) algorithms described in these papers are available at Florian Luisier's software repository.
2D SURE-LET Image Deconvolution
A Matlab implementation of the algorithm described in this paper: download the zip archive.
This algorithm uses the SURE-LET approach initially developed for image denoising, and extends it to image deconvolution. The deconvolution process is linearly parametrized by using multiple Wiener filters as elementary functions, followed by undecimated Haar-wavelet (subband-dependent) thresholding.
More details...2D and 3D PURE-LET Image Deconvolution
Matlab and ImageJ implementations of the algorithm described in this paper: download the 2D Matlab, 3D Matlab, or 2D ImageJ zip archive.
This algorithm extends the SURE-LET deconvolution approach to Poisson+Gaussian noise, typically for a fluorescence microscopy application
More details...Iterative LET Image Deconvolution
A Matlab implementation of the algorithm described in this paper: download the zip archive.
This algorithm solves a standard l1 restoration problem by an iterative approximation of the equivalent processing as a linear combination of "thresholds". The implementation is available for a deconvolution problem, regularized with the l1 norm of the wavelet coefficients of the image (redundant/non-redundant setting).
More details...Blur-SURE for Parametric Image Restoration
A Matlab implementation of the algorithm described in this paper: download the zip archive.
The problem considered here is the blind restoration of an image from noisy distorted samples, when the noise follows a Gaussian additive statistics, and when the distortion is an unknown, but parametrizable, linear operator (e.g.., convolution).
More details...Fourier-Argand Representation
Matlab implementation of demos using the representation described in this paper: download the zip archive.
The problem considered here is the construction of steerable filters for the detection of arbitrary patterns. The Fourier-Argand representation is the shortest steerable basis for a given approximation accuracy, and the basis filters can be obtained using a combination of Radon and Fourier transformations.
More details...Complex Wave Retrieval from a Single Interferogram
Matlab implementation of the algorithm described in this paper: download the zip archive.
The problem considered here is the reconstruction of a complex wave from its interferences with a reference wave, stored in an interferogram. The algorithm developed provides increased resolution compared to standard approaches, while allowing the intensity of the object wave to be similar to that of the reference wave, and significant overlap between zeroth and first Fourier order.
More details...Super-Resolving a Frequency Band
Matlab implementation of the "trick" described in this paper: download the MatLab m-file.
We introduce a simple formula that provides the exact frequency of a pure sinusoid from just two samples of its Discrete-Time Fourier Transform (DTFT). Even when the signal is not a pure sinusoid, this formula still works in a very good approximation (optimally after a single refinement), paving the way for high-resolution frequency tracking of fastly-varying signals, or simply improving the frequency resolution of the peaks of a Discrete Fourier Transform (DFT).
More details...