A Constrained Convex Optimization Approach to Hyperspectral Image Restoration with Hybrid Spatio-Spectral Regularization

Abstract

We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problems, consisting of a regularization term(s) and a data-fidelity term(s). The methods have to handle a regularization term(s) and a data-fidelity term(s) simultaneously in one objective function; therefore, we need to carefully control the hyperparameter(s) that balances these terms. However, the setting of such hyperparameters is often a troublesome task because their suitable values depend strongly on the regularization terms adopted and the noise intensities on a given observation. Our proposed method is formulated as a convex optimization problem, utilizing a novel hybrid regularization technique named Hybrid Spatio-Spectral Total Variation (HSSTV) and incorporating data-fidelity as hard constraints. HSSTV has a strong noise and artifact removal ability while avoiding oversmoothing and spectral distortion, without combining other regularizations such as low-rank modeling-based ones. In addition, the constraint-type data-fidelity enables us to translate the hyperparameters that balance between regularization and data-fidelity to the upper bounds of the degree of data-fidelity that can be set in a much easier manner. We also develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) to efficiently solve the optimization problem. We illustrate the advantages of the proposed method over various HS image restoration methods through comprehensive experiments, including state-of-the-art ones.

Distributed Compressed Hyperspectral Sensing Imaging Incorporated Spectral Unmixing and Learning

“…In this section, we report the performance of the proposed DCHI_SUL framework compared with 6 recently developed conventional and state-of-the-art hyperspectral compressed imaging methods, including STNCS [8], JT-3DTV [9], E-3DTV [12], HSSTV [17], DCHS [39], and DCS_SLM [40]. DCHS and DCS_SLM are the DCS framework.…”

“…Traditional model-based reconstruction methods exploit HSI structures by employing structure-inducing regularizers through handcrafting. Sparsity in some orthogonal transformation domains and total variation (TV) minimization of images are the two most commonly used prior knowledge [6,8,9,[13][14][15][16][17]. Typically, the cost functions of such model-based reconstruction methods consist of a data fidelity term and a single constraint or combination of multiple regularization terms capturing various assumed objection properties.…”

“…However, it is difficult to effectively constrain the optimal subspace for data recovery with a single prior. erefore, hybrid spatio-spectral total variation (HSSTV) [17] constructed a TV regularization item containing various difference operators of HSIs, such as spatial difference operators in horizontal and vertical directions, spatial difference operator, and spatial-spectral difference operator. Although excellent reconstruction performance was achieved, determining the proportion of each difference in the regularization item for different data is very difficult.…”

Survey on compressed sensing reconstruction method for3Ddata

“…Reference 110 also used HSSTV as a regular term to eliminate the effects of noise and artifacts. The difference is that the author uses data fidelity as a hard constraint for reconstruction, which can balance the relationship between noise and reconstruction accuracy better and prevent overfitting.…”

Image Motion Measurement and Image Restoration System Based on an Inertial Reference Laser

“…Non-blind restoration algorithms have made considerable progress in the field of image restoration. Several representative non-blind restoration algorithms have achieved ideal image restoration effects in their respective application fields, such as the Wiener filtering algorithm [ 34 ], total variation regularized image restoration algorithm [ 35 , 36 , 37 ], hybrid spatio-spectral total variation image restoration algorithm [ 38 ],image restoration algorithm based on the natural image gradient distribution model [ 39 ], and fast non-blind restoration algorithm based on natural image gradient constraints [ 40 ]. The authors in [ 41 ] proposed a local piecewise regularization Richardson Lucy (RL) method and constructed a new regularization term that effectively controlled the noise and edge ringing effect in the restored image.…”