In this paper, we propose a new framework to visualize hyperspectral images. We present three goals for such a visualization: 1) preservation of spectral distances; 2) discriminability of pixels with different spectral signatures; 3) and interactive visualization for analysis. The introduced method considers all three goals at the same time and produces higher quality output than existing methods. The technical contribution of our mapping is to derive a simplified convex optimization from a complex nonlinear optimization problem. During interactive visualization, we can map the spectral signature of pixels to red, green, and blue colors using a combination of principal component analysis and linear programming. In the results, we present a quantitative analysis to demonstrate the favorable attributes of our algorithm.