In the last decade, illumination problem has been the bottleneck of robust face recognition system. Extracting illumination invariant features becomes more and more significant to solve this issue. However, existing works in this field only consider the variations caused by lighting direction or magnitude (denoted as homogeneous lighting), while the spectral wavelength is always ignored in most of the developed illumination invariant descriptors. In this paper, we claim that the spectral wavelength is important, and we propose a novel gradient based descriptor, namely Logarithm Gradient Histogram (LGH), which takes the illumination direction, magnitude and even the spectral wavelength together into consideration (denoted as heterogeneous lighting). Our proposal contributes in the following three-folds: (1) we incorporate homogeneous filtering to alleviate the illumination effect for each image and extract two illumination invariant components, namely logarithm gradient orientation (LGO) and logarithm gradient magnitude (LGM); (2) we propose an effective postprocessing strategy to guarantee the fault-tolerant ability and generate a histogram representation to integrate both LGO and LGM; (3) we present thorough theoretical analysis on the illumination invariant properties for our proposed method. Experimental results on CMU-PIE, Extended YaleB and HFB databases are reported to verify the effectiveness of our proposed method.