This paper proposes an image restoration method using a convolutional sparse coding (CSC) unrolling network with a box constraint and total variation. Unlike conventional deep unrolling methods, the proposed method constructs an interpretable lightweight network with restoration stability. Specifically, we design a new constrained convex optimization problem that incorporates CSC, a box constraint, and total variation (TV). The box constraint ensures that the image values fall within a certain range, making the restoration process stable. In addition, combining total variation and CSC leads to high interpretability and representation with a small number of parameters. We develop an optimization algorithm based on the primal-dual splitting (PDS) method. Then, by unrolling the algorithm, we construct the proposed lightweight network. Experimental results demonstrate the superiority of the proposed method in image restoration accuracy and lightweightness of the proposed network in the number of parameters.

This paper proposes a method for sampling graph signals by designing a flexible sampling operator via a difference-of-convex (DC) based algorithm. Departing from conventional methods limited to bandlimited signals, our method extend the generalized sampling theory to handle graph signals beyond bandlimitedness. Our method aims to design a flexible sampling operator that mixes vertex values, while controlling the number of sample-contributive vertices. The operator design is formulated as a feasibility problem with an invertibility constraint for the best possible recovery and a constraint controlling the number of sample-contributive vertices. We reformulate the problem as a DC-like optimization problem by using the nuclear norm to obtain a tight relaxation of the invertibility constraint. To solve this problem, we present a DC-based algorithm. The effectiveness of our approach is demonstrated through sampling and recovery experiments on various graph signal models.

We propose a hyperspectral (HS) anomaly detection method using a novel characterization of anomalies. Among HS anomaly detection approaches, decomposition-based methods, which simultaneously estimate a background part and an anomaly part from an HS image, have attracted much attention. In these methods, various approaches have been proposed for mathematical modeling of the background part, but the anomaly part is mostly modeled by an ℓ1-norm or an ℓ2,1-norm. However, these norms have limited ability to promote the exact sparsity of the anomaly part, leading to detection failure. In this paper, we introduce a difference-of-convex (DC) approach to HS anomaly detection. First, we design a DC function that properly models the sparsity of the anomaly part. Next, we formulate a constrained DC optimization problem that decomposes a given HS image into the two parts and noise. Then, we develop an efficient solver for the problem based on the proximal linearized DC algorithm (PLDC) and the preconditioned primal-dual splitting method (P-PDS). Finally, we demonstrate the effectiveness of our method compared to state-of-the-art methods through experiments on several HS anomaly detection datasets.

This paper proposes a novel spatiotemporal (ST) fusion framework for satellite images, named Robust Optimization-based Spatiotemporal Fusion (ROSTF). ST fusion is a promising approach to resolve a trade-off between the temporal and spatial resolution of satellite images. Although many ST fusion methods have been proposed, most of them are not designed to explicitly account for noise in observed images, despite the inevitable influence of noise caused by the measurement equipment and environment. Our ROSTF addresses this challenge by formulating noise removal and ST fusion as a unified optimization problem. First, we define observation models for satellite images that may be contaminated with random noise, outliers, and/or missing values. Next, we introduce certain assumptions that naturally hold between the observed images and the target high-resolution image. Then, based on these models and assumptions, we formulate the fusion problem as a constrained optimization problem and develop an efficient algorithm based on a preconditioned primal-dual splitting method for solving the problem. The performance of ROSTF was verified using simulated and real data. The results show that ROSTF performs comparably to several state-of-the-art ST fusion methods in noiseless cases and outperforms them in noisy cases.

Spatiotemporal fusion (ST fusion) is a feasible solution to resolve a tradeoff between the temporal and spatial resolutions of satellite images. Although many ST fusion methods have been proposed, most methods have not been developed that explicitly take noise in observed images into account, despite the inevitable influence of noise caused by the observation equipment and environment. In this paper, we propose an optimization-based ST fusion method that is robust to noise. First, we introduce observation models for noisy satellite images and make certain assumptions on the relationship between the observed images and the target high-resolution image. Next, based on these models and assumptions, we formulate the fusion problem as a constrained optimization problem and develop an efficient algorithm based on a primal-dual splitting method for solving the problem. The performance of the proposed method was verified using simulated and real data, and the results illustrate that our method outperforms state-of-the-art ST fusion methods for both noiseless and noisy satellite images.

We propose an efficient foreground-background separation (FBS) method for (possibly noisy) video data. Most existing FBS methods model the background as a low-rank component. However, this approach is computationally expensive because it requires matrix/tensor decomposition of high-dimensional videos. In this paper, we first introduce a new background model, named static scene constraint (SSC), to FBS. SSC plays a role in accurately capturing the static background by keeping the temporal gradient of the background component to zero. In addition, SSC is formulated as a convex constraint using differences in the temporal direction, which eliminates the need for matrix/tensor decomposition in optimization and significantly reduces the computational cost compared to existing low-rank-based background models. Second, we formulate the FBS problem as a convex optimization problem involving SSC and develop an efficient solver based on a preconditioned primal-dual splitting algorithm, which can automatically determine the appropriate stepsizes based on problem structure. Finally, we demonstrate the efficiency and effectiveness of our method compared with state-of-the-art FBS methods through experiments using infrared and electron microscope videos.

The spatio-spectral total variation (SSTV) model has been widely used as an effective regularization of hyperspectral images (HSI) for various applications such as mixed noise removal. However, since SSTV computes local spatial differences uniformly, it is difficult to remove noise while preserving complex spatial structures with fine edges and textures, especially in situations of high noise intensity. To solve this problem, we propose a new TV-type regularization called Graph-SSTV (GSSTV), which generates a graph explicitly reflecting the spatial structure of the target HSI from noisy HSIs and incorporates a weighted spatial difference operator designed based on this graph. Furthermore, we formulate the mixed noise removal problem as a convex optimization problem involving GSSTV and develop an efficient algorithm based on the primal-dual splitting method to solve this problem. Finally, we demonstrate the effectiveness of GSSTV compared with existing HSI regularization models through experiments on mixed noise removal. The source code will be available at https://www.mdi.c.titech.ac.jp/publications/gsstv.

Removing stripe noise, i.e., destriping, from remote sensing images is an essential task in terms of visual quality and subsequent processing. Most existing destriping methods are designed by combining a particular image regularization with a stripe noise characterization that cooperates with the regularization, which precludes us to examine and activate different regularizations to adapt to various target images. To resolve this, two requirements need to be considered: a general framework that can handle a variety of image regularizations in destriping, and a strong stripe noise characterization that can consistently capture the nature of stripe noise, regardless of the choice of image regularization. To this end, this article proposes a general destriping framework using a newly introduced stripe noise characterization, namedflatness constraint (FC), where we can handle various regularization functions in a unified manner. Specifically, we formulate the destriping problem as a nonsmooth convex optimization problem involving a general form of image regularization and the FC. The constraint mathematically models that the intensity of each stripe is constant along one direction, resulting in a strong characterization of stripe noise. For solving the optimization problem, we also develop an efficient algorithm based on a diagonally preconditioned primal-dual splitting algorithm (DP-PDS), which can automatically adjust the step sizes. The effectiveness of our framework is demonstrated through destriping experiments, where we comprehensively compare combinations of a variety of image regularizations and stripe noise characterizations using hyperspectral images (HSIs) and infrared (IR) videos.

This paper proposes an effective and efficient destriping method for remote-sensing data. Destriping of remote-sensing data is an essential task because stripe noise not only degrades the visual quality but also seriously affects subsequent processing. We formulate the destriping problem as a convex optimization problem involving zero-gradient constraints, where the constraints are designed to exploit the fact that the spatial and temporal gradients of stripe noise equal to zero. Our method imposes such strong constraints on stripe noise, and thus can fully capture the nature of stripe noise, leading to very effective destriping. Also, operations required for handling the zero-gradient constraints in optimization are simple, which enables us to develop an efficient algorithm for solving the problem by a primal-dual splitting method. We demonstrate the advantages of our method over existing methods on destriping experiments using remote-sensing data.