Spatial Sparsity Regularization Research Articles

Multi-energy CT reconstruction using tensor nonlocal similarity and spatial sparsity regularization.

Multi-energy computed tomography (MECT) based on a photon-counting detector is an emerging imaging modality that collects projections at several energy bins with a single scan. However, the limited number of photons collected into the divided, narrow energy bins results in high quantum noise levels in reconstructed images. This study aims to improve MECT image quality by minimizing noise levels while retaining image details. A novel MECT reconstruction method was proposed by exploiting the nonlocal tensor similarity among interchannel images and spatial sparsity in single-channel images. Similar patches were initially extracted from the interchannel images in spectral and spatial domains, then stacked into a new three-order tensor. Intrinsic tensor sparsity regularization that combined the Tuker and canonical polyadic (CP) low-rank decomposition techniques were applied to exploit the nonlocal similarity of the formulated tensor. Spatial sparsity in single-channel images was modeled by total variation (TV) regularization that utilizes the compressibility of gradient image. A new MECT reconstruction model was established by simultaneously incorporating the intrinsic tensor sparsity and TV regularizations. The iterative alternating minimization method was utilized to solve the reconstruction model based on a flexible framework. The proposed method was applied to the digital phantom and real mouse data to assess its feasibility and reliability. The reconstruction and decomposition results in the mouse data were encouraging and demonstrated the ability of the proposed method in noise suppression while preserving image details, not observed with other methods. Imaging data from the digital phantom illustrated this method as achieving the best intuitive reconstruction and decomposition results among all compared methods. They reduced the root mean square error (RMSE) by 89.75%, 50.75%, and 36.54% on the reconstructed images compared with analytic, TV-based, and tensor-based methods, respectively. This phenomenon was also observed with decomposition results, where the RMSE was also reduced by 97.96%, 67.74%, 72.05%, respectively. In this study, we proposed a reconstruction method for photon counting detector-based MECT, using the intrinsic tensor sparsity and TV regularizations. Improvements in noise suppression and detail preservation in the digital phantom and real mouse data were validated by the qualitative and quantitative evaluations on the reconstruction and decomposition results, verifying the potential of the proposed method in MECT reconstruction.

Multiple-Speaker Localization Based on Direct-Path Features and Likelihood Maximization With Spatial Sparsity Regularization

This paper addresses the problem of multiple-speaker localization in noisy and reverberant environments, using binaural recordings of an acoustic scene. A Gaussian mixture model (GMM) is adopted, whose components correspond to all the possible candidate source locations defined on a grid. After optimizing the GMM-based objective function, given an observed set of binaural features, both the number of sources and their locations are estimated by selecting the GMM components with the largest priors. This is achieved by enforcing a sparse solution, thus favoring a small number of speakers with respect to the large number of initial candidate source locations. An entropy-based penalty term is added to the likelihood, thus imposing sparsity over the set of GMM priors. In addition, the direct-path relative transfer function (DP-RTF) is used to build robust binaural features. The DP-RTF, recently proposed for single-source localization, was shown to be robust to reverberations, since it encodes inter-channel information corresponding to the direct-path of sound propagation. In this paper, we extend the DP-RTF estimation to the case of multiple sources. In the short-time Fourier transform domain, a consistency test is proposed to check whether a set of consecutive frames is associated to the same source or not. Reliable DP-RTF features are selected from the frames that pass the consistency test to be used for source localization. Experiments carried out using both simulation data and real data gathered with a robotic head confirm the efficiency of the proposed multi-source localization method.

Accelerating multi-echo water-fat MRI with a joint locally low-rank and spatial sparsity-promoting reconstruction.

Our aim was to demonstrate the benefits of using locally low-rank (LLR) regularization for the compressed sensing reconstruction of highly-accelerated quantitative water-fat MRI, and to validate fat fraction (FF) and [Formula: see text] relaxation against reference parallel imaging in the abdomen. Reconstructions using spatial sparsity regularization (SSR) were compared to reconstructions with LLR and the combination of both (LLR+SSR) for up to seven fold accelerated 3-D bipolar multi-echo GRE imaging. For ten volunteers, the agreement with the reference was assessed in FF and [Formula: see text] maps. LLR regularization showed superior noise and artifact suppression compared to reconstructions using SSR. Remaining residual artifacts were further reduced in combination with SSR. Correlation with the reference was excellent for FF with [Formula: see text] = 0.99 (all methods) and good for [Formula: see text] with [Formula: see text] = [0.93, 0.96, 0.95] for SSR, LLR and LLR+SSR. The linear regression gave slope and bias (%) of (0.99, 0.50), (1.01, 0.19) and (1.01, 0.10), and the hepatic FF/[Formula: see text] standard deviation was 3.5%/12.1s[Formula: see text], 1.9%/6.4s[Formula: see text] and 1.8%/6.3s[Formula: see text] for SSR, LLR and LLR+SSR, indicating the least bias and highest SNR for LLR+SSR. A novel reconstruction using both spatial and spectral regularization allows obtaining accurate FF and [Formula: see text] maps for prospectively highly accelerated acquisitions.

Hyperspectral imagery super-resolution by compressive sensing inspired dictionary learning and spatial-spectral regularization.

Due to the instrumental and imaging optics limitations, it is difficult to acquire high spatial resolution hyperspectral imagery (HSI). Super-resolution (SR) imagery aims at inferring high quality images of a given scene from degraded versions of the same scene. This paper proposes a novel hyperspectral imagery super-resolution (HSI-SR) method via dictionary learning and spatial-spectral regularization. The main contributions of this paper are twofold. First, inspired by the compressive sensing (CS) framework, for learning the high resolution dictionary, we encourage stronger sparsity on image patches and promote smaller coherence between the learned dictionary and sensing matrix. Thus, a sparsity and incoherence restricted dictionary learning method is proposed to achieve higher efficiency sparse representation. Second, a variational regularization model combing a spatial sparsity regularization term and a new local spectral similarity preserving term is proposed to integrate the spectral and spatial-contextual information of the HSI. Experimental results show that the proposed method can effectively recover spatial information and better preserve spectral information. The high spatial resolution HSI reconstructed by the proposed method outperforms reconstructed results by other well-known methods in terms of both objective measurements and visual evaluation.