Not the least of President Carter's problems is the analysis of his problems. For the best evidence - that is the evidence of his wife Rosalynn and of his good friend Charles Kirbo - suggests that the president believes his record is unappreciated and that his standing will improve with better public presentation.

In fact, Mr. Carter's difficulties arise from deep causes not readily comprehensible. The one sure thing is that he has worked himself and the country into a plight that does not lend itself to a quick fix.

Mrs. Carter unburdened herself in an interview with The New York Times. She apparently concentrated on widespread misconceptions entertained about the president by the American public. She said:

"They think he is incompetent - he is not incompetent. They think he is indecisive - he is not indecisive. He is very strong, he is very determined, he knows what he wants and he doesn't back down, but he knows that in politics you have to compromise."

In explaining those misconceptions, Mrs. Carter fell back on the old chestnut about the news media. Among other things she blamed the press and television for conveying the impression that there was dissension within the ranks, and that the president was "surrounded all the time by Georgia people."

Mr. Kirbo gave his view in an interview with the National Journal. He, too, found fault with the image of uncertainty and indecision.

"I don't see how a man can get that image," he said, "which is just the reverse of what he is." Kirbo also blamed the news media. He said: "I think [Carter's image] is a reflection of what people hear on TV to a large extent and read in the newspaper to a lesser extent. I suppose it is our fault for not carrying on a publicity campaign and portraying him the way we know him."

The trouble with both sets of comments is that they pose a deep question and come up with a shallow answer. It is truly puzzling that a person as gritty and decisive as Carter would acquire the reputation of being hesitant and unsure of himself. Explaining how that impression arose requires not a knee-jerk response about the media, but probing and self-examination.

My impression is that the difficulties go back to the first months of the Carter administration. During that period Carter made a number of monumental blunders that grew out of campaign commitments.

One blunder, for example, was the hit list on water projects. The president decided to oppose the projects against the recommendation of experienced and highly placed associates, including Vice President Walter Mondale. By ignoring their advice, Carter created the coalition of Republicans and Democrats from the producing states of the South and West, which has been hamstringing his legislative program ever since.

Another clear blunder was the proposal for comprehensive arms control presented to the Soviet Union in March of last year. While in line with Carter's campaign stance, that proposal was not even among the suggestions advanced by the State and Defense departments. It was rejected out of hand by the Russians who have, ever since, nursed deep suspicions of the Carter administration.

On both of those issues, as on not a few others, the president was forced to retreat in highly visible ways. He is still retreating, which is why the impression has grown that he is indecisive and hesitant.

The prevailing impression, while surely wrong, cannot be undone merely by assertions or better public relations. For Carter is not now, as he was during the campaign, writing on a blank slate.

The present misconception grows out of an earlier illusion - the illusion fostered during the campaign that Carter has a prescription for the country's ills. Events have caused the public to change its mind, to conclude that the president does not have the answers. So it will take events to unsay that judgment, to persuade the public that Carter really is competent.

If a visible crisis were at hand, the president could show his stuff by managing it in ways satisfactory to everybody. As it happens, no such crisis is on the horizon. So Carter can retrieve his position only by truly difficult feats, such as holding back inflation and producing a settlement in the Mideast.

That is the hard way, to be sure. But the president does himself and the country no service by nourishing the illusion that there lies - in manipulating the public image - an easy way.