HIGHER DEGREE TOTAL VARIATION (HDTV) REGULARIZATION FOR IMAGE RECOVERY
HIGHER DEGREE TOTAL VARIATION (HDTV) REGULARIZATION FOR IMAGE RECOVERY
We introduce novel image regularization penalties to overcome the practical problems associated with the classical total variation (TV) scheme. Motivated by novel reinterpretations of the classical TV regularizer, we derive two family es of functional involving higher degree partial image derivatives; we term these families as isotropic and anisotropic higher degree TV (HDTV) penalties, respectively. The isotropic penalty is the mixed norm of the directional image derivatives, while the anisotropic penalty is the separable norm of directional derivatives. These functionals inherit the desirable properties of standard TV schemes such as invariance to rotations and translations, preservation of discontinuities, and convexity. The use of mixed norms in isotropic penalties encourages the joint sparsity of the directional derivatives at each pixel, thus encouraging isotropic smoothing. In contrast, the fully separable norm in the anisotropic penalty ensures the preservation of discontinuities, while continuing to smooth along the linelike features; this scheme thus enhances the line like image characteristics analogous to standard TV. We also introduce efficient majorize–minimize algorithms to solve the resulting optimization problems. The numerical comparison of the proposed scheme with classical TV penalty, current second-degree methods, and wavelet algorithms clearly demonstrate the performance improvement. Specifically, the proposed algorithms minimize the staircase and ringing artifacts that are common with TV and wavelet schemes, while better preserving the singularities. We also observe that anisotropic HDTV penalty provides consistently improved reconstructions compared with the isotropic HDTV penalty.
Existing System:
The reconstruction of images from their noisy measurements is an important problem in several areas, including remote sensing, biomedical imaging, astronomy, and radar imaging. In many practical applications, the measurement process is modeled by a linear operator, which is often ill conditioned.
In such cases, the standard approach is to use prior image information to constrain the solutions. Image recovery is often formulated as an optimization problem, where the criterion is a linear combination of data consistency error and a regularization penalty. The regularization functional is designed to penalize images that do not exhibit desirable properties (e.g., piecewise smoothness and sparsity).
The total variation (TV) smoothness prior is widely used in several practical applications, mainly due to its desirable properties such as convexity, invariance to image shifts and rotations, and ability to preserve edges.
Proposed System
The main goal of this paper is to introduce penalties involving higher degree derivatives, which inherit the desirable properties of the classical TV penalty (e.g., feature-preserving smoothing, invariance to rotation and translation, convexity, and simplicity). While the use of functionals that combine first- and second-degree derivatives of the image may provide better edge preservation, as reported in, we will focus on derivatives of a single degree in this paper for simplicity.
We introduce fast majorization–minimization (MM) algorithms to solve the anisotropic and isotropic HDTV regularized recovery problems. This approach is similar to iteratively reweighted (also termed as lagged diffusivity) algorithms used in standard TV minimization. The algorithm proceeds by successively minimizing a sequence of quadratic surrogate penalties.
Software Requirements:
.Net
Front End – ASP.Net
Language – C#.Net
Back End – SQL Server
Windows XP
Hardware Requirements:
RAM : 512 Mb
Hard Disk : 80 Gb
Processor : Pentium IV
FUTURE WORK:
Comparisons of the proposed regularization functional with classical TV penalty, current second-degree functional and sparse wavelet schemes in a range of practical applications demonstrated the significant improvement in performance.
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