Hyperspectral Image Compression Employing a Model of Anomalous Pixels

Anomaly Detection and Reconstruction From Random Projections

“…Thus, again, we have . Since these , , and are necessarily in the set searched by the maximization on the left side of (21), we have (23) The inequalities in (22) and (23) thus establish (21), and a similar argument for the hypothesis provides (24) As a consequence, the GLRT of (19) can be equivalently constructed in the projected domain as (25) At this point, we observe that (20) has the same form as (8), and (25) has the same form as (9), with , , and replacing , , and , respectively. As a consequence, the analysis in [10] applies verbatim, meaning that the test in (25) can be reduced to an expression similar to (10), namely (26) Like (11), the resulting RX anomaly detector then becomes (27) where and are the sample mean and covariance, respectively, of .…”

“…We observe that the straightforward encoder-side approach of [8] and [9]-preserving anomalies by first detecting them and then separately compressing them-is infeasible for sensors in which the random projections occur simultaneously with signal acquisition. Consequently, we focus on anomaly detection located at the decoder side of the system along with signal reconstruction.…”

“…A straightforward approach to accommodate anomalies is to detect them in advance of compression and store or transmit them separately along with their location (e.g., [8] and [9]). However, anomaly detection is typically a fairly computationally expensive task that may not be amenable to encoder-side processing in severely resource-constrained sensors [6].…”

Multitemporal Hyperspectral Image Compression

“…We note that the CR approach we consider here is similar to the anomaly removal proposed in [16] and [17] for the preservation of anomalies in JPEG2000 compression of hyperspectral imagery. In particular, the interpolation process we use is identical to that of [17].…”

An operational approach for hyperspectral image compression

“…In [7], hyperspectral compression with the goal of anomaly preservation was proposed. In [7], anomalies are first detected and then preserved without compression as overhead in the compressed bitstream; the remainder of the image is encoded using a traditional coder (e.g., PCA+JPEG2000 or SubPCA+JPEG2000). Before encoding, anomalous pixels are replaced by interpolation from neighboring pixels; in the decoding step, the original anomalous pixels are replaced back.…”