In a bowl, mix together your artichokes, peppers, mustard and capers. Set aside.
Slice each salmon fillet in half, lengthwise, as if you're planning to use each half as the top and bottom to "sandwich" the filling. When you're complete, each salmon fillet should be split into two thin sheet-like slices. Set them aside.
On a large platter or cutting board, lay a single slice of bacon. Then, parallel and slightly overlapping the first slice of bacon, lay a second slice of bacon. Continue this bacon "shingling" process, until you've used 3 or 4 slices of bacon (depending on the width of the bacon and the length of your salmon). This process should result in a rectangular "sheet" of bacon.
Season both sides of each of your salmon fillet halves with salt and pepper. Don't overdo it, though. Bacon is already salty. Just a little should suffice.
Lay one half of a salmon salmon at the top of the sheet of bacon, with the salmon running counter to the strips of bacon.
Use ¼ of the filling and spread it evenly over the salmon.
Add the top half of this particular salmon fillet, creating a "salmon sandwich".
Tightly roll the "salmon sandwich" into the bacon and set aside.
Repeat the above steps for the second salmon fillet.
Place a large, oven proof, sauté pan (large enough to hold all 4 salmon fillets, with room to spare) on the stove, over a medium-hot temperature, to begin pre-heating.
When all the salmon has been seasoned, stuffed and wrapped, carefully lay them into the hot sauté pan, with the seam side down. The salmon should sear for about 1 minute. Do not let the pieces touch each other. There should be space between each of them, to allow for better heat distribution, between the portions.
Transfer the entire pan, with the salmon, into the oven.
Let the salmon roast for about 15 minutes. Poke it with your finger. It should feel firm, but not "hard". With a meat thermometer, test the thickest part of each salmon. When each one has reached an internal temperature of 125° F, pull the pan out of the oven and allow them to rest for 10 minutes. This will allow the salmon to relax, while it also continues to (carryover) cook and come up to an internal temperature of about 130° F.