"Background" Reboot?

[fredfillis]

Over the past few days, my Pi has appeared to be occasionally locked up but, on further investigation, appears to have rebooted but the screen was not updated.
If I look in kern.log I can see the following:

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Jun  4 14:17:16 Raspbian01 kernel: imklog 5.8.11, log source = /proc/kmsg started.
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] Booting Linux on physical CPU 0x0
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] Initializing cgroup subsys cpu
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] Initializing cgroup subsys cpuacct
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] Linux version 3.10.24+ (dc4@dc4-arm-01) (gcc version 4.7.2 20120731 (prerelease) (crosstool-NG linaro-1.13.1+bzr2458 - Linaro GCC 2012.08) ) #614 PREEMPT Thu Dec 19 20:38:42 GMT 2013
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] CPU: ARMv6-compatible processor [410fb767] revision 7 (ARMv7), cr=00c5387d
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] CPU: PIPT / VIPT nonaliasing data cache, VIPT nonaliasing instruction cache
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] Machine: BCM2708
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] cma: CMA: reserved 16 MiB at 1e000000
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] Memory policy: ECC disabled, Data cache writeback
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] On node 0 totalpages: 126976
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] free_area_init_node: node 0, pgdat c05cfd5c, node_mem_map c067d000
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000]   Normal zone: 992 pages used for memmap
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000]   Normal zone: 0 pages reserved
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000]   Normal zone: 126976 pages, LIFO batch:31
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] pcpu-alloc: s0 r0 d32768 u32768 alloc=1*32768
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] pcpu-alloc: [0] 0
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] Built 1 zonelists in Zone order, mobility grouping on.  Total pages: 125984

To this noob, that looks like the start of a reboot. But the video on the screen is an image last displayed by my fbi slideshow. It is like the Pi reboots in the background if that makes any sense.
If I look at syslog, it appears that we suddenly skip back in time:

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Jun  4 14:16:01 Raspbian01 /USR/SBIN/CRON[4544]: (pi) CMD (date >> /home/pi/frame/memlog && free -m >> /home/pi/frame/memlog)
Jun  4 14:17:01 Raspbian01 /USR/SBIN/CRON[4584]: (root) CMD (   cd / && run-parts --report /etc/cron.hourly)
Jun  4 14:18:01 Raspbian01 /USR/SBIN/CRON[4627]: (pi) CMD (date >> /home/pi/frame/memlog && free -m >> /home/pi/frame/memlog)
Jun  4 14:20:01 Raspbian01 /USR/SBIN/CRON[4703]: (pi) CMD (date >> /home/pi/frame/memlog && free -m >> /home/pi/frame/memlog)
Jun  4 14:22:01 Raspbian01 /USR/SBIN/CRON[4779]: (pi) CMD (date >> /home/pi/frame/memlog && free -m >> /home/pi/frame/memlog)
Jun  4 14:24:01 Raspbian01 /USR/SBIN/CRON[4855]: (pi) CMD (date >> /home/pi/frame/memlog && free -m >> /home/pi/frame/memlog)
Jun  4 14:26:01 Raspbian01 /USR/SBIN/CRON[4931]: (pi) CMD (date >> /home/pi/frame/memlog && free -m >> /home/pi/frame/memlog)
Jun  4 14:28:01 Raspbian01 /USR/SBIN/CRON[5007]: (pi) CMD (date >> /home/pi/frame/memlog && free -m >> /home/pi/frame/memlog)
Jun  4 14:30:01 Raspbian01 /USR/SBIN/CRON[5083]: (pi) CMD (date >> /home/pi/frame/memlog && free -m >> /home/pi/frame/memlog)
Jun  4 14:17:16 Raspbian01 kernel: imklog 5.8.11, log source = /proc/kmsg started.
Jun  4 14:17:16 Raspbian01 rsyslogd: [origin software="rsyslogd" swVersion="5.8.11" x-pid="1855" x-info="http://www.rsyslog.com"] start
Jun  4 14:17:16 Raspbian01 kernel: [    0.000000] Booting Linux on physical CPU 0x0

How can my screen not be cleared by a reboot? How can I figure out what is causing this reboot?