Restoration of ultrasound images using spatially-variant kernel deconvolution

Mihai I. Florea (1) , Adrian Basarab (2, 3) , Denis Kouamé (2) , Sergiy A. Vorobyov (1)

1 Aalto University
2 IRIT-MINDS - CoMputational imagINg anD viSion
3 UT3 - Université Toulouse III - Paul Sabatier

Most of the existing ultrasound image restoration methods consider a spatially-invariant point-spread function (PSF) model and circulant boundary conditions. While computationally efficient, this model is not realistic and severely limits the quality of reconstructed images. In this work, we address ultrasound image restoration under the hypothesis of piece-wise linear vertical variation of the PSF based on a small number of prototypes. No assumption is made on the structure of the prototype PSFs. To regularize the solution, we use the classical elastic net constraint. Existing methodologies are rendered impractical either due to their reliance on matrix inversion or due to their inability to exploit the strong convexity of the objective. Therefore, we propose an optimization algorithm based on the Accelerated Composite Gradient Method, adapted and optimized for this task. Our method is guaranteed to converge at a linear rate and is able to adaptively estimate unknown problem parameters. We support our theoretical results with simulation examples.

Mots clés: Accelerated Composite Gradient Method; Point-spread function; Reconstruction; Restoration; Spatially varying; Ultrasound

Domaines: Traitement du signal et de l'image [eess.SP]

Mihai I. Florea, Adrian Basarab, Denis Kouamé, Sergiy A. Vorobyov. Restoration of ultrasound images using spatially-variant kernel deconvolution. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2018), Apr 2018, Calgary, Canada. pp.796-800. ⟨hal-02348205⟩