In holographic data storage, information is recorded within the volume of a holographic medium. Typically, the data is presented as an array of pixels with modulation in amplitude and/or phase. In the 4-f orientation, the Fourier domain representation of the data array is produced optically, and this image is recorded. If the Fourier image contains large peaks, the recording material can saturate, which leads to errors in the read-out data array. In this paper, we present a coding process that produces sparse ternary data arrays. Ternary modulation is used because it inherently provides Fourier domain smoothing and allows more data to be stored per array in comparison to binary modulation. Sparse arrays contain fewer on-pixels than dense arrays, and thus contain less power overall, which reduces the severity of peaks in the Fourier domain. The coding process first converts binary data to a sequence of ternary symbols via a high-rate block code, and then uses guided scrambling to produce a set of candidate codewords, from which the most sparse is selected to complete the encoding process. Our analysis of the guided scrambling division and selection processes demonstrates that, with primitive scrambling polynomials, a sparsity greater than 1/3 is guaranteed for all encoded arrays, and that the probability of this worst-case sparsity decreases with increasing block size.