Closed-form subband allocation for high-capacity and visually faithful image steganography

High-capacity image steganography must reconcile payload density with visual imperceptibility and statistical security. Uniform bit-depth embedding across transform subbands often induces a capacity staircase effect, where marginal depth increments cause disproportionate distortion. This study presents a subband-adaptive framework combining parameterized integer wavelet transform (PIWT), bounded coefficient adjustment (MOPAP), and closed-form rate-distortion allocation. A two-level decomposition separates low- and high-frequency subbands, assigning optimal embedding depths based on their relative distortion contribution. Instead of stochastic meta-heuristics, the allocation problem is formulated as a discrete rate-distortion objective solved by enumerating a bounded space of at most 216 candidate states. This provides a deterministic, certifiably global solution: parameter search is a constant-time bounded enumeration ( ≤ 0.20 ms, O ( 1 ) complexity), while embedding and extraction remain linear O ( N ) coefficient traversals. Two strategies are evaluated: an AllBand mode maximising throughput and a High-Frequency-Only mode for classical statistical transparency. On eight standard 512 × 512 images, the AllBand scheme achieves up to 4.1 bpp with PSNR ≥ 33.0 dB and mean SSIM of 0.84 (ranging from 0.72 on smooth to 0.94 on textured content). Histogram, difference histogram (PDH), and RS analyses indicate that bounded adjustment leaves no artefacts detectable by classical statistical screening. Across twelve literature baselines, analytical allocation outperforms fixed-depth schemes in 33 of 34 matched-capacity comparisons. Security claims are strictly scoped to classical statistical screening; detectability under deep-learning steganalysis is theoretically characterized via algebraic parity-locked micro-jumps.