Online convolutional dictionary learning for multimodal imaging

Abstract

Computational imaging methods that can exploit multiple modalities have the potential to enhance the capabilities of traditional sensing systems. In this paper, we propose a new method that reconstructs multimodal images from their linear measurements by exploiting redundancies across different modalities. Our method combines a convolutional group-sparse representation of images with total variation (TV) regularization for high-quality multimodal imaging. We develop an online algorithm that enables the unsupervised learning of convolutional dictionaries on large-scale datasets that are typical in such applications. We illustrate the benefit of our approach in the context of joint intensity-depth imaging.K. Degraux (email: kevin.degraux@uclouvain.be) is with ISPGroup/ICTEAM, FNRS, Université catholique de Louvain, 1348, Louvain-la-Neuve, Belgium. This work was completed while he was with Mitsubishi Electric Research Laboratories (MERL).

Convolutional Dictionary Learning: A Comparative Review and New Algorithms

“…Due to the structure ofD, which consists of concatenated diagonal matricesD m , linear system Eq. (19) can be decomposed into a set of N K independent linear systems [7], each of which has a left hand side consisting of a diagonal matrix plus a rank-one component, which can be solved very efficiently by exploiting the Sherman-Morrison formula [8].…”

“…This linear system can be decomposed into a set of N independent linear systems, but in contrast to Eq. (19), each of these has a left hand side consisting of a diagonal matrix plus a rank K component, which precludes direct use of the Sherman-Morrison formula [5]. We consider three different approaches to solving these linear systems:…”

“…The Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) [33], an accelerated proximal gradient method, has been used for CSC [6], [5], [19], and in a recent online CDL algorithm [18], but has not previously been considered for the dictionary update of a batch-mode dictionary learning algorithm.…”

Convolutional Dictionary Regularizers for Tomographic Inversion

“…where G is a 2-D finite difference operator and λ LPF controls the strength of the filter [28]. There are several algorithms for efficiently solving the CDL problem [13][14][15][16][17]. We consider three different variants of the CSC problem for white-noise denoising.…”

“…As a result there has been a revival of interest in the use of shift-invariant [8] models for images, also called convolutional sparse representation (CSR) models [9,10]. Recent work on efficient algorithms for convolutional sparse coding (CSC) [11,12] and the corresponding convolutional dictionary learning (CDL) problem [13][14][15][16][17] have allowed for the use of CSR as regularizers for a variety of inverse problems [18][19][20][21].…”