This paper proposes a new optimization framework for the joint optimization of sparsity and filter order (JOSFO) for FIR filter design. Since the cost function for JOSFO involves ℓ ₀ and non-uniform overlapped group ℓ ₀ norms, which are not convex, a global optimal solution is difficult to obtain. To find an approximate solution of the non-convex problem, existing approaches repeat the following steps: 1) approximate the cost function; 2) find candidates of zero coefficients by minimizing the cost function; and 3) set them to zero. On the other hand, this paper directly solves the optimization problem, without any approximation to the cost function, by using the alternating direction method of multipliers with the pseudo-proximity operators of ℓ ₀ and non-uniform non-overlapped group ℓ ₀ norms. Experimental results show that resulting filters designed by the proposed method have sparser coefficients and lower orders, while satisfying filter specifications, such as an error from a desired frequency response.

Pixel-domain weighting methods for multiple-exposure blending can efficiently remove noise and under-/over-exposed pixels simultaneously in high dynamic range (HDR) image generation. Various types of noise such as non-Gaussian noise, e.g., Poisson, impulse noise, and pixel saturation, are often superimposed to multiple-exposure images taken with a high ISO setting in a low-light condition. Because almost all existing methods assume Gaussian noise, these methods cannot sufficiently reduce these types of noise. To achieve high-quality HDR image generation in such difficult conditions, we propose a novel multiple-exposure blending method in which image blending is performed in a wavelet domain so as to enhance the denoising performance. In addition, the Huber loss function is utilized as a fidelity measure in blending to make the method robust against outliers. We also introduce an efficient algorithm based on a primal-dual splitting method for solving our optimization problem. The experimental results demonstrate the advantages of the proposed method over several conventional methods.

Hyperspectral (HS) image analysis has gained significant attention due to its ability to capture detailed spectral information across hundreds of bands, making it useful for environmental monitoring and mineral exploration applications. However, detecting anomalies in HS images, especially in complex scenes, remains challenging. This paper proposes a novel approach for robust anomaly detection by integrating tensor robust principal component analysis (TRPCA) with autoencoding adversarial networks (AEAN). Our method utilizes the AEAN model to learn a nonlinear low-dimensional representation of the spectral characteristics of background regions, which is then incorporated into the TRPCA framework. The TRPCA is further enhanced by incorporating prior knowledge of the sparsity of anomalous regions, enabling more accurate separation of background and anomaly components. This integration, achieved through a plug-and-play alternating direction method of multipliers (PnP-ADMM), significantly improves detection accuracy and robustness. Experimental results on benchmark datasets widely used for HS anomaly detection confirm that the proposed method consistently outperforms conventional techniques, achieving superior area-under-the-curve (AUC) scores across diverse and complex scenes. By leveraging both nonlinear modeling of background characteristics and sparsity-based anomaly separation, this research provides a more accurate and robust solution for HS anomaly detection, highlighting its potential for practical applications in remote sensing.

In this paper, we propose robust image-smoothing methods based on ${\mathit{\ell }}_0$ gradient minimization with novel gradient constraints to effectively suppress pseudo-edges. Simultaneously minimizing the ${\mathit{\ell }}_0$ gradient, i.e., the number of nonzero gradients in an image, and the ${\mathit{\ell }}_2$ data fidelity results in a smooth image. However, this optimization often leads to undesirable artifacts, such as pseudo-edges, known as the “staircasing effect”, and halos, which become more visible in image enhancement tasks, like detail enhancement and tone mapping. To address these issues, we introduce two types of gradient constraints: box and ball. These constraints are applied using a reference image (e.g., the input image is used as a reference for image smoothing) to suppress pseudo-edges in homogeneous regions and the blurring effect around strong edges. We also present an ${\mathit{\ell }}_0$ gradient minimization problem based on the box-/ball-type gradient constraints using an alternating direction method of multipliers (ADMM). Experimental results on important applications of ${\mathit{\ell }}_0$ gradient minimization demonstrate the advantages of our proposed methods compared to existing ${\mathit{\ell }}_0$ gradient-based approaches.

We present an algorithm for the constrained design of FIR filters with sparse coefficients. In general, the filter design approach aims to minimize a filter order and maximize the filter performance. Although the FIR filter coefficients designed by the least squares method is optimal in the least squares sense, it is not necessarily optimal among the set of filters with the same number of multipliers, that is, less mean squared error can be achieved by a filter that has the same number of multipliers, but has longer impulse response with some zero-valued entries. Our method minimizes the number of nonzero entries in the impulse response together with the least squares error of its frequency response. In addition, we incorporate some constraints to the design and realize better performance than conventional constrained least squares design.

Dynamic mode decomposition (DMD) is a powerful tool for separating the background and foreground in videos. This algorithm decomposes a video into dynamic modes, called DMD modes, to facilitate the extraction of the near-zero mode, which represents the stationary background. Simultaneously, it captures the evolving motion in the remaining modes, which correspond to the moving foreground components. However, when applied to noisy video, this separation leads to degradation of the background and foreground components, primarily due to the noise-induced degradation of the DMD mode. This paper introduces a novel noise removal method for the DMD mode in noisy videos. Specifically, we formulate a minimization problem that reduces the noise in the DMD mode and the reconstructed video. The proposed problem is solved using an algorithm based on the plug-and-play alternating direction method of multipliers (PnP-ADMM). We applied the proposed method to several video datasets with different levels of artificially added Gaussian noise in the experiment. Our method consistently yielded superior results in quantitative evaluations using peak-signal-to-noise ratio (PSNR) and structural similarity (SSIM) compared to naive noise removal methods. In addition, qualitative comparisons confirmed that our method can restore higher-quality videos than the naive methods.