In this paper, we propose a novel algorithm for processing the non-convex l0≤p≤1 semi-norm minimization model under the gradient descent framework. Since the proposed algorithm only involves some matrix-vector products, it is easy to implement fast implicit operation and make it possible to take use of the advantage of l0≤p≤1 semi-norm based model practically in large-scale applications which is a hard task for common procedure for l0≤p≤1 semi-norm optimization such as FOCUSS. The simulation of image compression and reconstruction shows the super performance of the proposed algorithm.
Although the current imaging sensors can achieve 12 or higher precision, the current display devices and the commonly used digital image formats are still only 8 bits. This mismatch causes significant waste of the sensor precision and loss of information when storing and displaying the images. For better usage of the precision-budget, tone mapping operators have to be used to map the high-precision data into low-precision digital images adaptively. In this paper, the classic histogram equalization tone mapping operator is reexamined in the sense of optimization. We point out that the traditional histogram equalization technique and its variants are fundamentally improper by suffering from local optimum problems. To overcome this drawback, we remodel the histogram equalization tone mapping task based on graphic theory which achieves the global optimal solutions. Another advantage of the graphic-based modeling is that the tone-continuity is also modeled as a vital constraint in our approach which suppress the annoying boundary artifacts of the traditional approaches. In addition, we propose a novel dynamic programming technique to solve the histogram equalization problem in real time. Experimental results shows that the proposed tone-preserved global optimal histogram equalization technique outperforms the traditional approaches by exhibiting more subtle details in the foreground while preserving the smoothness of the background.