Training-Free No-Reference Image Quality Assessment Using a Content-Independent Graph Fourier Watermark

<title>Abstract</title> <p>Deciding whether an image still looks acceptable normally requires the original, and in almost every setting where quality actually has to be monitored the original is long gone. This is the ordinary situation for any organisation that publishes visual material at scale: lecture recordings, slide captures, diagrams and scanned readings are re-encoded by the delivery platform, re-compressed by a content delivery network and degraded again by the connection at the far end, while the master copy stays on the origin server where the damage cannot be seen. Watermarking offers a way around this. A known pattern is planted before the image leaves the source, travels the same path, absorbs the same damage, and the state it arrives in stands in for the state of the image. Two influential schemes built this idea on the discrete wavelet transform and later on set-partitioning trees with content-adaptive bitplane selection. This paper keeps their estimation machinery and replaces the transform with a fixed Block-Graph Fourier Transform derived from the pixel-adjacency graph of an 8 × 8 block. Because that graph never inspects pixel values, the basis is identical at the embedder and at the blind receiver and no side information is transmitted. One watermark bit per block is embedded by quantization-index modulation into eight coefficients of a single mid-frequency band; a single global quantization step keeps all 39 evaluation images at or above 40 dB PSNR, averaging 42.65 dB. At the receiver, three no-reference features read off the recovered watermark — bit error rate, a soft confidence score and a residual second moment — are fused into one degradation index, mapped through an Ideal Mapping Curve fitted only on calibration images, and refined by a per-image closed-loop step. Across seven distortion families and four full-reference metrics the closed loop lowers the error in all 28 combinations tested, and Fisher-transformed confidence intervals separate the before and after correlations in 22 of them. PSNR is estimated to within 0.35–0.73 dB on five of the seven families. The estimator needs no training data and no subjective labels, and the paper is explicit about the one family where it does not win.</p>